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**Number Series**

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

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

Solution. (a) The numbers are multiplied by 2 to get the next number.

64 × 2 = 128

Difference Series:

Solution. (d) The difference between the numbers is 3.

15 + 3 = 18

Solution. (b) Previous number × = Next number

(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

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

The next number is 92 + 1 = 82

Solution. (d) The series is 22 – 1, 32 –1, 42 – 1,52 – 1. etc.

The next number is 62 – 1 =35

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

The next number is 62 + 6 = 42

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

The next number is 62 – 6 = 30

Solution. (a) The series is 13, 23, 33 , 43, etc.

The next number is 53 = 125

(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

(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

Solution. (a) The series is 13 + 1, 23 + 2, 33 + 3, etc.

The next number is 53 + 5 = 130

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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