Series - Tricks & Shortcuts for 2026 - 2027 Placement tests, Job Interviews & Exams

welcome to a logical reasoning video on series from career right.com this is an important topic of placement test job interviews and entrance exams where many candidates struggle they are not able to quickly find the relation in the series and hence they waste a lot of time on the question many even at the end leave the question and some of them don't even attempt the question but today we'll see some approaches and tips to quickly solve the questions on series along with this you can check out latest job offer rings in the market on Career right.com

the profile which you submit will be shared directly by us with the employers you will also get to know of interview experiences shared by other candidates so now let's start with [Music] series first let us take a look regarding types and tips of series okay now over here types means series can be of three major types okay 99% sums are related to this only one is numeric that is related to numbers second is alphabets that is letters and the third one is alpha numeric that is letters Plus numbers combination of letters and numbers and the

fourth type is uh generally as that is symbols we are not going to deal with it because generally symbols has no log logic whatever logic is needed for solving symbol series it is already given in the question okay so no need to consider symbols over here here we will focus on the most important topics where 99% sums are asked that is numbers letters and letter numbers or alpha numeric right now series sums can be asked in three formats okay these are three types there are three formats of sums one is find the next number in

the series or find the next group of uh letters or next letter in the series then is find the missing number or the missing alphabet or the missing group of alphabets the third one is find the odd man out or find the odd number or the odd alphabet or the odd group within the given Series right now we have seen the types we have seen some the format of questions over here in the types these types these three types have many subcategories okay these subcategories are you have already seen these subcategories it's nothing big in

it we are going to see each and every subcategory so that you will be able to understand what kind of sums are asked and how to approach them okay now let's move on to some tips regarding series while approaching the series sum please understand the first thing you have to do is to find the relation between the given elements okay and second sum is using the relation solve the question and get the answer now how to find a relation okay or what kind of relation we should search now whenever we are talking about finding a

relation let us assume that this is a series 3 4 5 6 this is a series now in it say if we take this element we have to find relation of this element with the previous element and the next element then if you move on to this element find the relation between previous element and next element if we move on to this element find the relation between previous element and next element then you'll get a pattern okay this pattern is what we need and using this pattern we can solve the question so now how to

go on or how to approach in finding the relation very easy what you need to do is that say the this is a series okay this is a series 1 2 3 4 5 6 and we have to find the pattern in it what you need to do first is let us find the difference between two elements okay in this is for only for the number series okay I'm not talking about letters and alpha numeric for that I'm going to tell you a different strategy for but for numbers it is important please pay attention over

here because this will help you get the series pattern very very quickly okay or easily now over here let us find the difference between two numbers 2 - 1 is 1 3 - 2 is 1 4 - 3 is 1 here you are seeing that there is a steady difference or a constant difference if the difference is not constant okay if the difference is like first there is a difference of one then between the second and third element the difference is of six say 7 then third and fourth the difference is suddenly 25 and fourth

and fifth difference is say 200 fifth and sixth difference is say 5,500 so this difference is increasing arbitrarily and it is very very huge it is not going steadily something like that it is increasing very very it is going very high there is a very steep rise in the difference in such cases always remember that the series must be related to square of number cube of number or multiplication okay or simple multiplications right if this is the case if the difference between the numbers or elements is very very high it is increasing very highly or

very quickly that means the series is related to squares of numbers cubes of numbers multiplication of numbers okay now we'll tell you what exactly we mean by square Cube multiplication but just remember this I'm going to repeat it afterwards also but still remember it if the difference is constant like this one one one or if the difference is uh increasing very slowly like here the difference is one then here the difference instead of one it becomes three then here the difference becomes say seven then here the difference becomes say 10 your difference becomes say 15

so it is increasing but it is slowly increasing it is not increasing very arbitrarily and all that stuff so over here in this scenario the series must be related to addition okay addition subtraction multiplication division multiplication division okay or the series might be of a prime numbers or it might be a Fibonacci Sequence I'll tell you what all these things are Fibonacci Sequence prime numbers addition subtraction okay but just listen to what I am saying so these might be the types there are many more okay miscellaneous types also are there or combinations is also there

so these these two rules which are there they are very very important while approaching a sum related to series always keep these rules in mind that is the reason I've told you right at the start okay now what we'll do is now we'll first see what are the type of series okay okay we'll see what is numeric series what is letters what is alpha numeric and then we'll try while solving the sums we'll try to understand how to approach the sums related to series okay a more detailed approach as to how to identify what kind

of series it might be okay moving on to the first type that is the numeric series number series numeric series or number Series has a lot of subcategories okay we'll denote a few prominent ones or the basic ones which are extremely important and most sums are related to that okay first one is related to addition or the addition series take a look at this example 19 25 32 40 question mark and we have 59 now in this series what we have learned first always find the difference 25 - 19 is 6 this is 6 32

- 25 is 7 40 - 32 is 8 that means that 19 + 6 you'll get 25 25 + 7 you'll get 32 32 + 8 you'll get 40 so here we are finding difference so here a pattern is emerging that first six is added then in the second element seven is added in the third element eight is added that is one more so in fourth element how much should be added + 9 okay then you'll get some answer over here and in that you'll add 10 and you'll get 59 so let's see whether we

are right or not 19 + 6 is 25 + 7 32 + 8 is 40 + 9 is 49 and 49 + 10 is 59 so this series looks complete it is following a pattern first six is added then seven then eight such kind of series is addition Series where things just are just added okay to the previous number you add something to get the next number again you add something over here to get the next number now here there have plus 6+ 7 + 8 + 9 + 10 okay they might even have ADD

+ 1 + 1 + 1 or + 2 + 2 + 2 or they might even add say odd numbers right so first they'll add one then they'll add directly three then they'll add five then they'll add seven then they'll add N9 only OD numbers might be added or only even numbers might be added addition can be of anything so when you determine that it is an addition series you just need to find out the pattern as to what exactly is being added same way you have the subtraction series okay in subtraction series instead of

addition it is subtraction for example 102 85 68 question mark 34 what is the difference 102 - 85 is 17 85 - 68 is 17 so 102 - 17 is 85 85 - 17 is 68 so here also it should be subtracting - 17 subtracting 17 that is 68 - 17 you'll get 51 again from here you subtract 17 and you'll get 34 so here a constant value has been subtracted okay so whenever a series is increasing it is addition or multiplication okay next number is greater than previous number okay so 32 is also greater

than 9 40 greater than 19 49 greater than 19 25 so it is increasing like this so it is addition or multiplication Series in subtraction the numbers decrease like this okay even in division the numbers will decrease right now next like addition subtraction like we have talked about right now multiplication Series in multiplication series The number is multiplied by some number to get the next number like I'll give you an example take a look at this series 1 2 6 24 120 1 to 2 okay what is the difference the difference is 1 6 difference

is 4 24 year difference is 18 20 - 24 120 - 24 difference 96 see the difference is increasing very very quickly that means this must be related to multiplication okay so let's try to think of some multiplication like 1 and two what is the relation 1 into 2 is 2 okay so we found this relation 1 into 2 is 2 2 and 6 what can might be the relation we know 2 into 3 is 6 correct now 6 and 24 what can be the relation 6 into 4 is 24 so what is happening is

that the next number which is there it is taken over here and it is multiplied by something it is first it is multiplied by first is multiplied by two then three then four so this must be multiplied by five right this should come over here and this must be multiplied by 5 so 24 into 5 becomes 120 right so what will be the next number write it 120 over here here it is 5 2 3 4 5 6 12 into 6 will give you 720 this is the answer this is multiplication it might also happen

that each of these uh each of the number is multiplied by a constant number okay like say 6 12 24 48 96 6 is multiplied by 2 you get 12 12 is again multiplied by 2 you get 24 24 is multiplied by 2 you get 48 48 is multiplied by 2 you get 96 okay such multiplication can also be there same way there is division there is nothing to it okay this is the division series take a look at it okay 216 72 36 12 question mark 2 okay here the difference which is there it

is falling okay here we saw if it is rising very quickly it is multiplication if it is falling very quickly exactly opposite that it is will be division okay let us see what division 26 when it is divided by 3 you'll get 72 72 when you divide by 2 you'll get 36 36 again when you divide by 3 you get 12 so divide by 3 divide by 2 divide by 3 divide by 2 answer here it will be 6 again divide by 3 3 2 3 2 3 you'll get answer as two so our answer

is correct the here it will come here the answer will be six this is division we are going to see examples of all of these so don't worry Don't Panic there's nothing to it it is very very easy now after these basic numeric series let us move on to some special numeric series now special numeric series I mean they are not that special I just said it for like effects purpose and all that stuff but over here see there are some numeric series which you should know for sure because many times sums are asked on

them the first one is regarding okay squares that is squares of a number squares cubes and the series which are near to it I'll explain what it means near to it and all that stuff okay you you must know squares of numbers squares up to 30 and you must know cubes of numbers up to 10 because it is very very useful to decifer the series also it would be useful for your Quant right so first of all let us see an example of square series or numbers near it say take a look at this series

zero okay not this 0 3 8 15 24 35 question mark 63 now if You observe closely what do we see over here difference is 3 - 0 is how much 3 8 - 3 difference is 5 here difference is 7 here the difference is 9 11 11 okay question we don't know over here so it is increasing okay it is steadily increasing right so this must be related to addition subtraction multiplication something like that now over here we have taken smaller values okay if we go on if you go on increasing over here you'll

realize that it is increasing more and more the difference is increasing more and more okay over here if You observe very closely this is zero 0 is nothing but 1 - 1 3 is nothing but 4 - 1 8 is nothing but 9 - 1 15 is 16 - 1 this is 25 - 1 this is 36 - 1 question mark we don't know this is uh 64 - 1 and this is nothing but 1 square 2 square 3 Square 4 Square 5 Square 6 Square uh so by default here it should be 7 Square

this is 8 square so 7 Square - 1 now you'll say that by looking directly at this how will we guess that it is a square series or something like that that is the thing of series whenever you get a series if you are not able to uh think about what series it might be you have to apply some tricks like okay is this nearer to some square is this nearer to some square is it a square of some number like that okay here it is 4 Square - 1 9 uh sorry it is 4

uh 2 - 1 3 Square - 1 4 Square - 1 all that stuff is given over here this is what we mean by square series or a series which is nearer to squares if you talk about cubes what you can have this is a cube series 64 125 216 3 43 okay observe carefully these this is 4 Cube this is 5 Cube this is 6 cub and this is 7 Cube okay these are the cubes so this is a series now after this take let's take a look at another very important special series and

that is nothing but prime number series okay you know what are prime numbers prime numbers are those numbers which are divisible by themselves n one apart from that no other number okay so we know one is not a prime number we prime number start with two two 3 5 7 11 13 17 19 and so on these are prime numbers this is the prime number series it might happen that they might give you an addition series okay and in that while adding first they'll add two then they'll add three then they'll add five then they'll

add seven okay so such kind of you need to find out what the addition is and then you need to see okay this is like prime numbers are getting added so after 7 11 is the next prime number so in the next element I have to add 11 after 11 13 is the next prime number so I have to add 13 in the next element to get the next element okay this is prime number series the numbers which are not prime are called as composite numbers okay the rest of them numbers like 4 6 8

okay 9 10 all 12 all these numbers are composite numbers because they are not prime now after prime number series a very important series I'm going to talk about that is the Fibonacci series now what do you mean by the Fibonacci series over here in Fibonacci series the best part about Fibonacci series is that say this is first second third fourth Fifth Sixth Element okay addition of this element and this element will give you this element if you want this element then add this and this you'll get this element okay if you want this element

you'll have to add this element to this element and then you'll get this element so fimon series always starts with two ones that is this see I I'll draw over here one and one Fibonacci Sequence starts with this and it goes on up to Infinity so this is the first element this is the second element so what is the next element add this and this what you'll get 1 + 1 is 2 what is the next element add the previous two elements 2 + 1 is 3 next 3 + 2 is 5 next 5 +

3 is 8 8 + 5 is 13 13 + 8 is 21 21 + 13 is 34 34 + 21 is 55 + is 89 89 + 55 is 144 and so on okay this is the Fibonacci sequence or the Fibonacci series so in exam okay or in paper they might give you the series right from here to here like that in between only so you just need to check whether addition of these two numbers is this these two numbers is this these two numbers is this this if that is the case that means that

it is a Fibonacci Sequence and you just need to add these two numbers to get the next number okay after Fibonacci Sequence I'm going to tell you a very important point please pay attention Okay it is really very important sometimes it might happen that a series is given like say 1 say 2 3 4 5 8 7 6 5 4 okay this series is given now here You observe it increases the here from 1 to 8 there is an increase 8 to2 there is a decrease 2 to7 increase 7 to3 there decrease so if there

is such increase decrease increase decrease that means that there are two possibilities one is there are two different series just like I wrote over here 1 2 3 4 5 and other series are out 8 7 6 5 4 there might be two different series or there is another possibility that is that two different operations are going on that means once it is getting here some addition is there and here subtraction is there here addition is there here subtraction is there something like that is going on okay so two two different operations are going on

or there are two different series we have to think in these ways we are going to see a example of it but still I'm telling you right now I'll explain it again during the example also apart from from this say if you're not able to understand how to solve a sum what you need to do is you just need to break the number and analyze each number individually that also we are going to see it might also happen that say if a series is a b c d e f so instead of giving directly ABC

they might write C B A they might reverse it okay f e d okay they might reverse it and give the series even that is the possibility you have to check that also okay so we have seen some of the series right now let's move on to uh we have seen numeric series let's move on to the alphabet series or the letter series alphabet series a bit easier than the number series or the numeric series and the thing that is going to help you a lot when it comes to alphabet series and alpha numeric series

is this A to Z you have to write always whenever you go to the exam always write a to z and their positions that is a comes first B is second Zed is 26 okay and reverse position this is another very important concept that you should know reverse position of the letters that means if Zed is considered as 1 y will be 2 x will be 3 and a will be 26 how to find reverse position we have checked that out in the previous logical reasoning uh videos okay but again I'll also tell you over

here total number of letters are 26 okay so what is 26 + 1 20 27 so if you want the reverse position of any alphabet just subtract the original position from 27 let's take a example D over here original position is four I want the reverse position of D 27 - 4 27 - 4 what is the answer 23 this is the reverse position of D this will become 24 this will become 25 and a will become 26 okay see how easy it is remember subtract the original position from 27 and you'll get the reverse

position when you go in exam always write this down write the reverse positions also so it becomes very easier to calculate okay now we'll see how this chart of A to Z helps in alphabet series later on while solving the sums but over here in alphabet series okay I'll draw a line over here okay there are two type of sums which majorly are asked 99% times these two types are there one is regarding vowels and consonants okay ws and ANS what are the vowels a e i o u okay A E I O U these

are the vowels and related to this the question might be asked or they'll omit the vowels and they'll just keep consonants that is the rest of the letters and a question would be asked on that and the second would be the position of the alphabet okay the alphabet which we have like a to z their position question might be on their position like first a is there okay then they'll skip two letters and directly write they'll skip B and C B and C is skipped and they'll write D again E and F two letters are

skipped and they'll write G like that so it is based on position right so there are many types in this we are going to see it in example but remember that there are only two types mostly and the best way to tole tackle the sums related to alphabet series is this chart a to zed now here so you should see the position of the first alphabet see the position of the next alphabet then the third alphabet there are two type of two type of sums that may be asked it might be like this A B

C D that is uh each element is just one letter and sometimes there may be groups instead of letters like a b c d e f g h i j k l and we have to find the next uh three letter letters okay so here what we have to do take the first letter find relation with the second letter take the second find relation with the fourth and also we have to find the relation of this group with this okay so such things are there it is very easy actually once you draw the chart you

will very easily be able to guess the answer or the pattern let's take a look at few examples so that it would become more and more clear now look at this example c e h okay question mark Mark then you have o q t then we have u w z we have to find what comes in place of question mark C this is the first letter Okay C is over here e one position second position so plus 2 you'll get e e f g h okay plus 2 again what you'll get no actually see d

e only one one over here only one skip is there and from E to H one skip second skip okay so two skips are there and then the third letter is written over here for o QT o again one skip o is over here one skip you get P okay one skip q and T one skip second skip there are two skips over here again here also one skip here also two skips between W and Zed so whatever answer will come over here okay whatever options would be given a b c d e what ever

options are there we have to see that in that option the whatever is given like for example they give uh say m o r we have to as a then we have to see if between M and o one skip is there and O and r two skips are there if it that is the case that will be our answer okay see how easy it is using this table or this whatever uh rough note you have written for of A to Z and the positions let's take another example b d a a f h e

then question mark then n p m now over here B and D what is the difference here B is over here B and D difference is one so there is only one skip Okay C has been skipped B skipping C then we get D okay then d and a now d a comes before D so one 1 before D is c 2 before D is B and 3 before D is a so what we can say between d and a the difference is min - 3 okay 1 2 and 3 this is the third so

minus 3 d 2 a when we go three places back we'll get a same way over here f g g has been skipped so plus one and directly we get H now H to e again one over here look at the table over here e and H 1 2 and 3 again minus 3 skip here also N2 P one Skip and P to M we have to go backwards three times that is minus 3 the third letter backwards would be M so whatever would be the answer over here we have to see that that group

has this pattern right + one and minus 3 now over here we have BDA we have fhe we have npn there must be some relation between this group and this group let us find out what the relation is you can there are two ways to think about it what you can think is that after a they have given directly F okay a to F what is the distance 1 2 3 4 okay four is the distance between a and f f is the fifth distance is four and fifth is f so distance is four now

e to the next letter now this group has 1 2 and three letters so distance between e and this first letter would be how much again four right what is it 1 2 2 3 and four it would be J so it has to be J over here also we have learned that from J okay when we Skip One the next one will be the second letter J Skip One don't write K it would be l l comes over here again from L we have to skip three in the opposite direction that is we have

to go reverse we have to go back three 1 2 and three what we get is I okay from I Now let us check this four okay whether it is four or not from I 1 2 3 and four we get n as the fifth so we are exactly right on track and we have decied it properly this is how you identify it now there is another logic to identify the connection between these two elements or these two elements let us see what over here what do we have we have BDA okay now we know

a comes before B so what we can write we can write this as a is there then B comes and then D comes we skip C and then D comes over here e is there then F comes then we skip G and H comes just like this over here I over here let's not go over here we'll go over here m is there then n comes then we skip o and then P comes correct this is also a logic also you can see d a then B then D and this after this d what comes

after d e e is over here at the last correct e f h h is over here what comes after h i I should be also here at the last then from I what comes is J we skip K and we get L after L what comes M comes so M must be here at the last which is already there after m n comes n skip o and we get p this is also a logic you can use any logic just get the right answer okay moving on to another series let us see h f

d okay n l j question mark question mark o x VT now let us see whether we can find some relation okay now h f d so H is over here f is over here D is over here oh we are going in the opposite direction H then F then e in the reverse direction we are going so let us now say let us see or we can what we can say is that one one skipping is there H they have skipped G then F they have skipped e and then D okay in opposite direction

so J is there where is J J is over here L okay J is over here l l is over here n is over here J they have skipped one k then they have gone to L they have skipped one then n right over here so here what is happening is that hfd we are going in opposite direction like this n l j okay first first is n then L again over here in opposite direction J L and N J Ln or n LJ right n LJ again we are going in this direction this we

don't know we have to go in this Direction only let us check from here T V and X first we or XV and T first we have X then we have V then we have t again we are going in this direction right so here also we'll go in the opposite direction o okay we don't know what is over here but we know o as the last element so we have to skip one since we are going in this direction this is the last element so we have to now go in this direction to find

the answer okay what comes before o we have to skip P we'll get Q over here okay again skip R we'll get S over here so answer is s qo if you try to Mark s qo you'll get S then we skip r q then pip R and O that is again we are going in this direction so our answer is correct answer is SQ instead of question mark SQ will come see how easy it becomes using the table of a to z now let us take a look at some of the alpha numeric series

alpha numeric Series has alphabets and numbers in it okay now again in alpha numeric series the most important part is this chart A to Z and the position of the alphabets as well as the reverse position positions okay and how to find reverse positions that we have seen subtract everything subtract the original position from 27 you'll get the reverse positions right now in alpha numeric series generally how to find out the relation I'll give you an example of alpha numeric Series right now over here so you'll understand what exactly we mean by alpha numeric Series

2 E2 1 H9 1 k6 then we'll have 1 N3 of find the next one this is one okay not I this is one now over here this is an alpha numeric Series where we have alphabets and numbers what to do whenever you find an alpha numeric series the first thing that you have to do is whatever numbers is there in the group or element you have to see if they are related to the position of the alphabet okay position or reverse position of the alphabet right so two and two if they are related to

position of e or not or reverse position of e or not that we have to to check now after that say if it is not related to position you have to find whether these numbers are related to each other like if there is each other okay I'll write it over here each other so you'll not forget make a note of this now two and two we know 2 is equal to 2 1 and 9 we don't know what relation it is there 1 and six again don't know what relation 1 and three don't know what

relation so over here we have to we try should try to find if they have any connection with each other okay now if that is not the case then try to find relation with numbers of other groups with numbers of numbers of other groups like for example here we have two and two okay two and two is it related to 1 and N is it related to 1 and 6 or 1 and 3 or this two related to one or this two related to 9 like that we have to try to find or what you

can do is take this as 22 take this as 19 something like that we have to find the relation okay now even if that is not possible then actually parallel to this we also should check out if the letters are connected to each other same thing we have to do for letters also right so whatever alphabets are there we have to find out the relation for those also and in this trial and error you'll get the pattern I now we'll see a example we'll solve this example also as well as we'll see another example example

as to what we are talking about now this sum which we are seeing or the question which we are seeing over here it can be solved in two ways there are two Logics you can use any logic okay I'll explain both the Logics over here two is there two is there what we have to check whether it is related to position of the letter so two and two no e position of e is five so 2 and two is not related what is reverse position of e 27 - 5 22 okay this two this two

this two this two let's check over here 1 n okay what is the reverse position of H 27 - 8 19 yes we are finding a pattern 1 N means 1 n over here so 16 13 these must be the reverse positions of the letters right so whatever option is there we have to check there we have to see if whatever the option is given it has the for example if the option is like this p and uh 2 say 0 9 or 9 0 if uh this is the reverse position of P then we

can select it as the correct option okay so check out the options now what is the second logic over here 2 and 2 is 22 1 and 9 is 19 1 and 6 is 16 1 and 3 is 13 If You observe closely what is happening is that -3 -3 -3 so by default next one will be - 3 this will be 10 so that means the three positions which are there this is one this is zero we have to to find the letter e and H E is over here H is over here there

is a gap of two okay they have skipped two letters H and K one letter skpt second letter skript K K and N one letter skript second letter script n n and next what is there one letter script second letter script Q so answer is Q so answer is 1 Q so this is the second way to solve the same sum you can use any number of ways just get the right answer let's take another example h8 L 12 O 15 s 19 and next one okay here h8 l12 o5 S1 19 is given what

is number check if it is related to position H position is 8 yes so eighth position is of H so h8 12th position is of L so L1 12 o5 O is 15 s is 19 what will be next now how to find next see if no options are given what you'll do or if in option say options I I'll give you four options so you'll understand what I'm talking about u21 v22 r18 and x24 okay now in all the four options uh the uh letter which is there and position is correctly given U is

21 V is 22 R is 18 x is 20 24 so what will be the correct answer how you will write now comes that the number has to be connected to the other numbers or the numbers of the other group this is one group this is second group third group so eight relation of 8 and 12 must be found out 12 and 15 must be found out 8 + 4 is 12 12 + 3 is 15 15 + 4 is 19 okay now here we are seeing a relation + 4 + 3 + 4 so

here it will be + 3 19 + 3 is 22 what is 22 V answer is v22 see how easy it is with the chart which is given okay so move moving on we'll see some of the sums related to series we'll solve them and we'll see how we are approaching the sums in exam also please don't forget to log to Career right.com to check out the latest jobs in the market go on to the job Forum of career right.com question number one 2 5 10 17 28 question question mark let us try to find

out what exactly is the next element in this series now first I will tell you what to do now whenever if you are not able to find the series uh directly or if you not able to tell what series It Is by Direct by observation what you can do is first try addition okay addition series try to see if it is an addition series then try if it is an subtraction series then try if it is a multiplication series then Division Series then see if there are prime numbers involved okay if all of them are

prime numbers or prime numbers are being added or subtracted multiplied something like that after that after prime numbers still you are not getting try for Fibonacci okay Fibonacci Sequence see if it is a Fibonacci Sequence right and even after this if you're are not getting whenever what you can try is that you can try a combination of all these methods right you will get the answer for sure most of 99% times you'll always get the answer from these methods now sometimes what will happen is that the series would be really huge like see I'll give

an example 4895 4897 4899 okay now I know they I'm just adding 2 two two but let us assume that this is a series and in this I'm not able to decifer and the numbers are also looking big so what to do what you can do over here is you can break this number into two parts 48 95 same way you can analyze this 48 you can analyze this 95 again divide it 48 95 you can see that 48 gets repeated okay 95 to 97 plus 2 is there okay over here also 48 repeated 97

to 99 + 2 is there so like this you can break that you can even break this 48 95 into 4 Parts this this this and check okay four gets repeated eight gets repeated N9 gets repeated 5 + 2 is 7 you can try to analyze this way also sometimes that if you see the series might be like this 58 995 then 68 95 so over here they might what they are just adding 1 1,000 or they what they might be doing is that 4895 if you reverse it you'll get 9 5 984 5 985

5 986 so this is also a series just like ABC they can write it as CBA a just to confuse you they might do it with numbers also so please pay attention let us solve the first sum 2 and five difference what we have learned first see what the difference is 2 to 5 difference is 3 5 to 10 it is 5 10 to 7 7 7 to 11 so what will be next over here if we see observe carefully these are nothing but odd numbers but what are the odd numbers 3 5 7 n

is also odd number but nine is not included then these must be some special kind of odd numbers or some special numbers If You observe carefully you'll know that these are prime numbers 3 5 7 11 so what is the next prime number 13 so 28 + 13 will be how much 40 1 okay 8 + 3 1 okay so 41 so next uh number which is there is 41 41 is our answer see how easy it is moving to the next question question number two let us see here you have to find the missing

element what is the difference 34 and 21 the difference is 13 34 and and 55 21 okay 55 and 8 34 okay now can you observe okay this also difference 55 Can You observe something in the difference you get 21 34 55 which are nothing but these numbers when such a thing happens directly you should know that it is a Fibonacci Sequence okay please remember very important right it is a Fibonacci Sequence how let's see 21 and 34 34 + 21 is 15 55 55 + 34 is 89 89 + 55 is 144 so this

will be what 144 + 89 what it will be 14489 9 + 4 13 1 4 12 13 233 is the answer 233 this will be the next number in the series moving on now next is l o j q h and have to find the other one okay I purposefully written this A to Z because in exam you'll always be having this in uh rough space okay and you can refer what is the first one it is L then is O then is J then is Q then is H so it is like we

are going this we are going this way again coming this way this way again coming this way this is like what we have seen in number series there is an increase there is a decrease there is an increase there is an decrease so that that means that two different operations might be happening over here or there are two different series okay so how the series might be it might be like this and this might be a series let us see l j h l where is J and H so we are going in this direction

L Skip One J Skip One H okay this is a sort of a pattern let's see the other one o q question mark we have o Skip One q and the other one what it will be as per this pattern we are going in this direction what will be the next one skip this s so answer is s see how easy it became even if there are two series they have combined it tried to make it difficult using this chart it becomes very easy to pinpoint or find the pattern and solve the question moving to

question number four USG question mark okay Where is u u s p l g okay over here can you see this much Gap this much Gap this much Gap this much Gap so you Skip One okay s then skip 1 and two then P then 1 2 3 three are skipped and then l 1 2 3 4 four are skipped then so skipping which is there we are going in opposite direction like this and skipping which is there first one is skip skipped then two are skipped then three letters are skipped then four letters are

skipped so now five letters must be skipped 1 2 3 4 five are skipped answer is a moving to question number five okay now we are here with question number five the wrong term question okay the Third Kind of sum which can be asked in series find the wrong term in the following series 10 14 28 34 64 68 136 10 and 4 difference is 4 4 and 28 difference is 14 28 and 34 difference is 6 34 and 64 difference is what what is the difference over here 30 64 and 68 difference is what

4 68 and 136 difference is what uh this is about 68 so now over here if you see two times we get a difference of four over here only there is a difference of six we have to find the wrong term in the series okay what happens over here 14 and 28 difference is 14 that means it is like sort of being doubled right it is being doubled over here also 68 136 difference is 68 so it is being doubled so say here it is four and then doubling is there here it is four and

doubling is there here it is four and doubling is there so there must be some problem over here here also it should be four and then doubling must be there okay so here what happens is that six is getting added then we get 34 say if we add 4 4 over here what you'll get over here 32 and difference between 32 is double is 64 so we are getting a very correct series that means the wrong term over here is 34 okay because of 34 what is happening we are finding that six is getting added

and only 30 is getting added we are not trying we are not getting this kind of relation four and double four and double okay so a common relation should be there we found what kind of relation might be there we were doubtful so what we did instead of after 28 instead of adding six we added four what we got as 32 double of 32 is 64 so what we have over here is the correct series will be 10 14 14 2 are 28 28 + 4 is 32 32 2 are 64 64 + 4 is

68 68 2 are 136 so we have add four and then multiplied by 2 okay moving to next question again find the wrong term okay 15 16 20 30 45 70 now we don't know how to start so let's see the difference here the difference is 1 16 - 15 1 20 - 16 4 30 - 20 10 45 - 30 15 okay 70 - 25 is how much this is 25 so over here okay difference is steadily little by little increasing it is not going too fast or something like that but if you see

there are some common numbers which when you see the first thing that you get to know is there's a specific thing that comes to your mind like for example whenever you see four you'll say Okay 2 square is 4 whenever you say 9 you say Okay 3 square is 9 whenever you see 25 you say 5 square is 25 or if you say 27 you'll immediately say 3 n are or 93 are is 27 or 3 cube is 27 like over here it comes it can be 1 square this can be 2 square this can

be 5 Square so there is problem between these two numbers only in this pattern okay there is a problem between these two numbers so this difference if it would have been n then this would have been 3 Square okay and if this if the difference is n that means this number has to be 29 then difference between 29 and 45 would be 16 what it would be 16 16 is nothing but 4 Square then the pattern is correct that means this number which is there it is not 30 it has to be 29 then only

we can get a nice series of 1 square 2 square 3 Square 4 Square 5 Square so the answer is 30 30 is the wrong term correct term should be 15 16 20 29 45 and 70 so the difference here becomes 1 here difference is 4 your difference is 9 year difference is 16 year difference is 20 5 this is 1 square 2 square 3 Square 4 Square 5 Square moving to question number 7 find the wrong term in the following series 1 3 10 21 63 129 now over here difference 3 - 1 is

2 10 - 3 is 7 21 here it is 11 63 - 21 is 52 42 okay 129 - 63 it is 2 use 9 - 3 is 6 12 - 6 60 six okay so here again the difference which is there it is increasing too much so this must be like here the see how it is to 7 directly 11 direct 42 direct 66 so it is increasing at a steady rate and quickly so this must be somehow related to multiplication but what multiplication 1 into 3 is 3 okay 1 is here 3 is

here 10 is here 21 63 129 1 into 3 is 3 but 3 is into 10 is not a multiple of three we at Max can write 3 into 3 is 9 and 9 + 1 but then over here again 10 into what uh 2 or 10 into 3 is 30 30 - 9 we'll have to do okay 30 - 9 10 into 3 - 9 then 21 into 3 is 63 so there's no as such direct relation when it comes to multiplication also but so the reason I've taken this example is to show you

how complex or how combination works okay let's see what is three say if we write 1 into 2 + 1 what you'll get 1 2 2 2 + 1 is 3 now after that now we have to come near 10 so 3 into 3 is 9 9 + 1 is 10 we have to come to 21 we have 10 into say 2 + 1 is 21 so over here it so happen is that this is multiplied by two this is by 3 again it is 2 let's see over here 21 * by 3 directly we

are getting 63 okay so here multiply by 2 + 1 is there multip by 3 + 1 is there multip by 2 + 1 is there so this should be multiply by 3 + 1 so answer should be 64 over here but still we'll check we'll check okay 64 2 3 2 3 2 64 into 2 + 1 64 into 2 is 128 + 1 is 29 so answer has to be 64 this is the wrong number okay see how uh when you see such a pattern 2 3 2 like that such when such pattern

is seen by you even if you don't have much enough evidence to prove it what you can do is you can take a hunch and you can try just like I did what I assume that okay this 63 might be wrong let us assume this pattern only and write 64 and let us see if the next number checks out okay such trial and error method is always needed in in series otherwise you won't get the answer quickly moving to question number eight here we have 3 2 8 12 13 24 18 okay so again up

down up down little bit up down is there so we can assume that there are two series or two operations are being done okay uh let us assume there are two series how the series might be it might be like this okay like this can you see 3 + 5 is 8 + 5 is 13 + 5 is okay okay so here we have + 5 + 5 + 5 next series what we will have 2 12 12 24 24 32 32 42 2 and 12 difference 10 12 and 24 difference 12 okay it can

be 10 added 12 added 14 added 24 and 32 difference 8 oh why why difference let's see 32 and 42 difference 10 so here we have two 10 so here it might be there might be some problem over here if this two is shifted over here you'll get 10 and 10 and you'll get us proper what we say proper Series so say if this is 12 and if we add 10 to it what you'll get you'll get 22 and 22 again when we add 10 to it what you'll get we'll get 32 so that means

the problem is over here okay correct Series has to be 3 2 8 12 13 and 22 then 18 32 23 they they will follow so what will happen 2 + 10 is 12 12 + 10 is 22 + 10 is 32 + 10 is 42 answer is 22 so correct answer is 24 24 is the wrong term moving to next question so here we have 1 11 34 75 139 question mark okay let us find the difference 11 - 1 is 10 34 - 11 is 23 okay 75 - 7 uh 75 - 3

4 is 41 139 - 75 is 9 - 5 is 4 13 - 7 is 6 so this is 10 so here I'm not able to find any relation directly so what I'll do is I'll use another method that I'm going to teach you now that is triangular method you can try to solve the sums by this way also try to find a pattern using this way also if you are not getting a pattern in the immediately in the second line what you can do is you can try to find the difference 23 - 10

13 41 - 23 18 64 - 41 23 okay again over here 13 and 18 difference is 5 18 2 difference is 5 see now here we have a pattern that 5 five is there so 13 + 5 is 18 18 + 5 is 23 then 10 + 13 is 23 23 + 18 is 41 41 + 23 is 64 so how to find the next one very very easy this is this is 5 this is 5 this will also be 5 so 23 + 5 will be how much 28 okay then 64 + 28

will be how much 8 + 4 2 6 + 1 7 8 9 92 okay and 139 + 92 would be how much 9 + 2 is 11 1 3 4 4 + 9 is 13 231 so 231 would be the next number this is known as triangular pattern if this is also a way of thinking this is not a way to solve any sum this is a way of thinking to find this is a way of uh finding the pattern or trying to see if we can find a pattern right just like we try

Square we like we try Cube we try the Triangular pattern also moving on okay here we have 28 33 31 question mark 34 39 okay so 20 difference 28 and 33 difference is 5 28 + 5 is 33 33 again it has gone down oh so it is up down up down so what we can do is that we uh let's see let's see first we don't know this middle number so we are not sure whether it is up down up down up down or whether this is only one incident let's see 33 and 31

what is the difference 2 okay so this is + 5 33 - 2 is 31 now here we don't know anything here we don't know anything 34 and 39 is + 5 so here we have + 5 here we have + 5 after + 5 we have -2 so it might be a series like this + 5 -2 + 5 -2 + 5 Okay so let's try whether this series is correct or not 28 + 5 33 - 2 is 31 + 5 would be 36 36 - 2 would be 34 34 + 5 would

be 39 so we are getting a valid series over here so 36 is the answer okay see how easy it is this is called as the combination of addition and subtraction Series right series is actually very easy if you just uh know how to approach them you just have to approach with confidence that you will get the answer try a com after trying the basic series of addition subtraction and all that stuff like Prime and Fibonacci try the combination also okay by most of the times I'll tell you in 95% times the basic series would

be enough you'll be able to deduce using the basic series and the Triangular pattern which we saw right now if you know the basic series like squares cubes and all that stuff 95% sums of Rel which are related to series would be solved by you just practice only practice will give you the uh expertise when it comes to Series so keep on practicing a lot this is it for series you can check other reasoning and quantitative aptitude tutorials on our Channel also check the job Forum on career right.com for latest jobs in the market share

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