# Number Series | Competitive Exam | Reasoning

### Definition:

In a number series question of reasoning, a series is given, with one number missing.

First of all, we will see how to find a missing term when we are given a sequence of numbers including one or more missing numbers. Hence, such a series follows a pattern, keeping this pattern in mind, we will have to find the missing term.

However, we shall also encounter questions on how to find the number that does not follow the pattern. In other words, we are given a sequence of numbers. The whole sequence except one number follows a certain rule. You have to find that number which does not follow the rule.

Lastly, questions related to series completion are giving in this blog. Therefore, these questions ask in Railway, Bank, SSC and all government jobs. Series completion questions are based on a special pattern of the series. You need to identify the patterns of the given series.

### Prime Number Series:

Example. 4, 9, 25, 49, 121, 169,…

(a) 324

(b) 289

(c) 225

(d) 196

Solution. (b) The given series is a consecutive square of prime number series. Therefore, the next prime number is 289.

### Multiplication Series:

Example. 4, 8, 16, 32, 64… 256

(a) 96

(b) 98

(c) 86

(d) 106

Solution. (a) The numbers are multiplied by 2 to get the next number.So, 64 × 2 = 128

### Difference Series:

Example. 3, 6, 9, 12, 15,…. 21

(a) 16

(b) 17

(c) 20

(d) 18

Solution. (d) The difference between the numbers is 3. 15 + 3 = 18

### Division Series:

Example. 16, 24, 36,… 81

(a) 52

(b) 54

(c) 56

(d) 58

Solution. (b) Previous number × = Next number

### n2 Series:

Example. 4, 16, 36, 64, …. 144

(a) 112

(b) 78

(c) 100

(d) 81

Solution.(c) The series is square of consecutive even numbers. 22, 42,62, 82 Next number is 102 = 100

### n2+1

(n2 + 1) Series Example. 17, 26, 37, 50, 65,….101

(a) 82

(b) 75

(c) 78

(d) 90

Solution. (a) The series is 42 + 1, 52 +1, 62 + 1, 72 + 1, 82 + 1. The next number is 92 + 1 = 82

### n2-1

(n2 -1) Series Example. 3, 8, 15, 24,…48

(a) 32

(b) 33

(c) 34

(d) 35

Solution. (d) The series is 22 – 1, 32 –1, 42 – 1,52 – 1. etc. The next number is 62 – 1 =35

### n2+n

(n2 + n) Series Example. 2, 6, 12, 20, 30,…. 56

(a) 32

(b) 34

(c) 42

(d) 24

Solution. (c) The series is 12 + 1, 22 + 2, 32 + 3, 42 + 4, 52 + 5, etc. The next number is 62 + 6 = 42

### n2-n

(n2 – n) Series Example. 0, 2, 6, 12, 20,….42

(a) 25

(b) 30

(c) 32

(d) 40

Solution. (b) The series is 12 – 1 = 0, 22 – 2 = 2, 32 – 3 = 6, etc. The next number is 62 – 6 = 30

### n3 Series

Example. 1, 8, 27, 64,…. 216

(a) 125

(b) 512

(c) 215

(d) 122

Solution. (a) The series is 13, 23, 33 , 43, etc. The next number is 53 = 125

### n3+1

(n3 + 1) Series Example. 2, 9, 28, 65,…217

(a) 123

(b) 124

(c) 125

(d) 126

Solution. (d) The series is 13 +1, 23 + 1, 33 + 1, etc. The next number is 53 + 1 = 126

### n3-1

(n3 -1) SeriesExample. 0, 7, 26, 63, 124,…

(a) 251

(b) 125

(c) 215

(d) 512

Solution. (c) The series is 13 – 1, 23 – 1, 33 – 1, etc. The next number is 63 – 1 = 215

### n3+n

(n3 + n) SeriesExample. 2, 10, 30, 68,….222

(a) 130

(b) 120

(c) 110

(d) 100

Solution. (a) The series is 13 + 1, 23 + 2, 33 + 3, etc. The next number is 53 + 5 = 130

### n3-n

(n3 – n) Series Example. 0, 6, 24, 60,…. 210

(a) 012

(b) 210

(c) 201

(d) 120

Solution. (d) The series is 13 – 1 = 0, 23 – 2 = 6, 33 – 3 = 24, etc. The next number is 53 – 5 = 120