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# What is Number Series in Reasoning ?

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## What is Number Series?

Number series is a arrangement of numbers in a certain order, where some numbers are wrongly put into the series of numbers and some number is missing in thatseries, we need to observe and find the accurate numberto the series of numbers.

In competitive exams number series are given and whereyou need to find missing numbers. The number series are come in different types. At first you have to decided whattype of series are given in papers then according with this you have to use shortcut tricks as fast as you can.

A series is an informally speaking of numbers. it is the sum of the terms of a sequence. Finite terms and series are defined by first and last terms while infinite series is endless. Number series is a form of series in which particular numbers are present in a particular order and missing numbers are to find out, nowadays number series is an important part of each and every government exams, especially in banks. It acquires a high weight.

A series is solved by particular number series tricks, formulas, attitudes of a person. There are various types of series present in the exam. Series can be of many types of Numbers like Natural numbers, Whole numbers, Contagious numbers etc. A sequence is described as a list of elements with a particular order.

Different types of Number Series?

There are multiple types of number series available —

Integer Number Sequences – There are particular formulas tricks to solve number series. Each number series question is solved in a particular manner. This series is the sequence of real numbers decimals and fractions. Number series example of this is like 1.3.5.9….. etc. in which what should come next is Solved by number series shortcuts tricks performed by the candidate.

Rational Number Sequences — These are the numbers which can be written as a fraction or quotient where numerator and denominator both consist of integers. An example of this series is %, %, 1.75 and 3.25.

Arithmetic Sequences — It is a mathematical sequence which consisting of a sequence in which the next term originates by adding a constant to its predecessor. It is solved by a particular formula given by the mathematics Xn = x1 +(n- 1)d. An example of this series is 3, 8, 13, 18, 23, 28, 33, 38, in which number 5 is added to its next number.

Geometric Sequences – It is a sequence consisting of a multiplying so as to group in which the following term starts the predecessor with a constant. The formula for this series is Xn= x1 rn-1. An example of this type of number sequence could be the following:

2, 4, 8, 16, 32, 64, 128, 256, in which multiples of 2 are there.

Square Numbers – These are also known as perfect squares in which an integer is the product of that integer with itself. Formula= Xn= n2. An example of this type of number sequence could be the following:

1, 4, 9, 16, 25, 36, 49, 64, 81, ..

Cube Numbers – Same as square numbers but in these types of series an integer is the product of that integer by multiplying 3 times. Formula= Xn=N3. Example:-1, 8, 27, 64, 125, 216, 343, 512, 729, …

Fibonacci Series — A sequence consisting of a sequence in which the next term originates by addition of the previous two

Formula = F0=0,F1=1

Fn = Fn-1 + Fn-2.

An example of this type of number sequence could be the following:

0, 1, 1, 2, 3,5, 8, 13, 21, 34, …

### Shortcuts – Tricks for Number Series

Number Series puzzles can be solved by various tricks provided by mathematics.

Firstly check the direct formulas as in like check

if all the numbers are prime, even or odd.

If all the numbers are perfect squares or cubes.

If all the numbers have a particular divisibility.

If all the numbers are succeeding by some additions or subtraction or multiplications or divisions by a particular number or addition of their cubes and squares. Number series methods are teaches by a professional to a student so that number series can be solved quickly and correctly. Now comes the Number series questions for IBPS Exam.

### How to Solve Number Series Problem?

Ans. As talked about over the number series problems are solved by some particular number series rules applied logically. There are various methods to solve number series like predict the next number ii.e which number will come next by applying rules like by adding, subtracting etc. or by applying various shortcut tricks.

Ans. There are various types of questions asked in bank exams :-

Type 1: In this kind of inquiries, a series of numbers is given with one number missing represented by a question mark. The Candidate has to select from the options available to correct option in place of the question mark.

The given sequences of numbers will be such that every number takes after its predecessor in the same way, i.e., according to a particular pattern. Hopefuls are required to figure out the right ways in which the sequence is formed and thereafter find out the number to finish the arrangement.

### How to solve questions on “Number Series”?

• Questions on number series give you a series of numbers which are all connected to each other. Once you have identified this pattern, solving the question becomes very simple.
• This pattern can be of various kinds. Check the section below for a list of common patterns which are frequently present in the Bank Exam.
• Once you have identified the pattern, apply it to the number before/ after the missing number in the series to get the desired answer.

Prime Series : IN which the terms are the prime numbers in Order

Ex: 2,3, 5, 7,11, 13,_, 19

Here the terms of the series are the prime numbers in order. The prime number after 13 is 17. So the answer to this question is 17.

Alternate Primes. :

Ex: 2, 5, 11, 17, 23, _, 41

Here the series is framed by taking the alternative prime numbers. After 23, the prime numbers are 29 and 31. So the answer is 31.

Every Third number can be the sum of the preceding two numbers.

Ex : 3, 5, 8, 13, 21

Here starting from third number

3+5=8

5+8=13

8+13=21

So, the answer is 13 + 21 = 34

Every Third number can be the product of the preceeding two numbers

Ex: 1, 2, 2, 4, 8,32. _

Here starting from the third number

1×2=

2×2=4

2×4=8

4X 8=32

So, the answer is 8 X 32 = 256

The difference of any term from its succeding term is constant (either increasing series or decreasing series :

Ex: 4, 7, 10, 13, 16, 19. _, 25.

Here the difference of any term from its succeding term is 3.

7-4=3

10-7=3

So, the answer is 19 + 3 = 22

The difference between two consecutive terms will be either increasing or decreasing by a constant number :

Ex : 2, 10, 26, 50, 82, _

Here, The difference between two consecutive terms are

10-2=8

26-10=16

50-26=24

82 – 50 = 32

Here, the difference is increased by 8 (or you can say the multiples of 8). So the next difference will be 40 (32 + 8). So, the answer is 82 + 40 = 122

Ex : 63, 48, 35, 24, 15, _

Here, the difference between the two terms are-

63-48 =15

48 -35=13

35-24=11

24-15=9

Here, the difference is decreased by 2. So, the next difference will be 7. So, the answer is 15-7 = 8.

The difference between two numbers can be multiplied by a constant number :

Ex: 15, 16, 19, 28, 55, _

Here, the differences between two numbers are

16-15=1

19-16=3

28-19=9

55-28=27

Here, the difference is multiplied by 3. So, the next difference will be 81. So, the answer is 55 + 81 = 136

The difference can be multiplied by numbers which will be increasing by a constant number :

Ex: 2, 3, 5, 11, 35, _

The difference between two numbers are

3-2=1

5-3=2

11-5=6

35-11=24

Here, the differences are multiplied by numbers which are in increasing order.

Differences are –

1

1×2=2

2×3=6

6×4=24

So, the next difference will be 24 x 5 = 120. So, the answer is 35 + 120 = 155.

Every succeeding term is got by multiplying the previous term by a constant number or numbers which follow a special pattern.

Ex: 5, 15, 45, 135, _

Here, 5x 3=15

15×3=45

45x 3=135

So, the answer is 135 x 3 = 405.

Ex: 2, 10, 40, 120, 240, _

Here, 2x 5=10

10×4=40

40 x 3=120

120 x 2 = 240

So, the answer is 240 x 1 = 240

In certain series the terms are formed by various rule (miscellaneous rules). By keen observation you have to find out the rule and the appropriate answer.

Ex: 4, 11, 31, 90, _

Terms are,

4×3-1=11

11×3-2=31

31×3-3=90

So, the answer will be 90 x 3 – 4 = 266

Ex : 3, 5, 14, 55, _

Terms are,

3×2-1=5

5×3-1=14

14x 4-1=55

So, the answer will be 55 x 5-1 = 274

Ex : 3, 7, 23, 95, _

Terms are,

3×2+1=7

7X3+2=23

23×4+3=95

So, the answer will be 95 x 5+ 4 = 479

Ex : 6, 17, 38, 79, _

Terms are,

6×2+5=17

17×2+4=38

38×2+3=79

So, the answer is 79 x 2+ 2=160.