### NUMBER SERIES

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 ½, ¾, 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 r n-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, … **Patterns in differences:**Calculate the differences between the numbers given in the series provided in the question. Then try to observe the**pattern in the new set of numbers**that you have obtained after taking out the difference.**For example –**2, 5, 8, 11, 14… (here the difference between the numbers is 3, hence the next number will be 17)**Pattern in Alternate numbers:**when there is a pattern between every**alternate or third number in the series****For example –**2, 9, 5, 12, 8 , 15, 11….**Odd One out:**when all but one number is part of a series**For example –**5, 10, 12, 15, 20… (Here all numbers except, 12 are multiples of 5)**Pattern in adjacent number:**when adjacent numbers in the series changes based on a logical pattern.**For example –**2, 4, 12, 48… (Here the first number is multiplied by 2, the second number by 3 and the third number by 4)**Complex series:**in some patterns the differences between numbers is**dynamic rather than being fixed**, but there still is a clear logical rule.**For example –**3, 4, 6, 9, 13, 18.. (Here you can add 1 to the difference between two adjacent items. After the first number add 1, after the second number add 2 and after the third number you can add 3)**Using two or more basic arithmetic functions:**in some series more than one operation (+, -, ÷, x) is used.**For example –**5, 7, 14, 16, 32… (here you can add 2, multiply by 2, add 2, multiply by 2, and so on)**Alternate Primes:**Here the series is framed by taking the**alternative prime numbers.****For example**2, 5, 11, 17, 23, _, 41**Every Third number can be the sum of the preceding two numbers:****For example**3, 5, 8, 13, 21Here starting from third number 3 + 5 = 8, 5 + 8 = 13, 8 + 13 = 21,

So, the answer is 13 + 21 = 34

**Decimal series**1250, 500, 200, 80, 32, 12.8, ?

Whenever you see a decimal number in series, your guess for the number should be a decimal digit or division process Here too a decimal number is multiplied or divided to form this series.

1250÷2.5 = 500

500÷2.5=200

200÷2.5= 80

80÷2.5=32

32÷2.5=12.8

12.8÷2.5=5.12

- n^2+1 series
- n^2-1 series
- n^2+n series
- n^2-n series

**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.

##### What Types of questions asked in bank exams related to number series?

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

Type I: 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.

**30, 34, 43, 59, 84, 120,?**

(1) 169

(2) 148

(3) 153

(4) 176

(5) None of these

Solution: (1) The given pattern is:

+22, 32, +42, + 62, +72

So, missing term is 169=120 +72**40, 54, 82, ?, 180 ,250**

(1) 142

(2) 124

(3) 136

(4) 163

(5) None of these

Solution: (2) The pattern is: +14, + 28, + 42, + 52, + 70

So, missing term is 82 + 42=124

Type 2 – In this we are given a sequence of number. The whole sequence, except the odd number, follow a certain rule. You need to search that number which does not follow the rule.

**0, 1,3,8,18,35,264**

(1) 62

(2) 35

(3) 18

(4) 8

(5) None of these

Solution: (1) The pattern is +(02+1), +(12+1), + (22+1) ,+ (32+1), + (42+1), + (52+1)

So, 62 is wrong and must be replaced by 35 + (52+1) = 62**1, 9, 125, 49, 729, 121, 2147**

(1) 2147

(2) 729

(3) 125

(4) 1

(5) None of these

Solution: (1)

**Some of the questions asked in number series previous papers –**

Directions: (1-5) In each of these questions a number series is given. In each series stand out number isn’t right. Discover the wrong number. (IBPS CWE PO/MT Exam 2012)

- 5531 5506 5425 5304 5135 4910 4621

(1) 5531

(2) 5425

(3) 4621

(4) 5135

(5) 5506

Solution: The number should be 5555 in place of 5531.

-72, -92, -112, -132, -152, -172…

Ans: (1) - 6 7 9 13 26 37 69

(1) 7

(2) 26

(3) 69

(4) 37

(5) 9

Solution: The number should be 21 in place of 26.

+1, +2, +4, +8, +16, +32

Ans: (2) - 1 3 10 36 152 760 4632

(1) 3

(2) 36

(3) 4632

(4) 760

(5) 152

Solution: The number should be 770 In place of 760.

×1 +2, ×2 +4, ×3 +6, ×4 + 8, ×5 +10, ×6 + 12, …

Ans: (4) - 4 3 9 34 96 219 435

(1) 4

(2) 9

(3) 34

(4) 435

(5) 219

Solution: The series is 02+ 4, 12+2, 32+0, 62-2, 102-4, 152- 6,212 – 8…

Hence, 435 should be replaced with 433

Ans: (1) **157.5 45 15 6 3 2 1**

(1) 1

(2) 2

(3) 6

(4) 157.5

(5) 45

Solution: The number should be 2 in place of 1.

3.5, 3, 2.5, 2, 1.5, 1, .