# Logical Reasoning - Number Series

## Number Series Description

In a number series questions, a series is given, with one number missing. In order to complete the series it is important to choose the correct alternative from the given ones that will complete the series. Number series questions are based upon the following concepts.

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. 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.
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) 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) 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) 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) 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) 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) Series
Example. 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) Series
Example. 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) 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

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