Home › Exam notes › SSC CGL › Number Series

Number Series

General Intelligence & Reasoning · Series (Number & Alphabet)

Useful for: SSC CGL

Overview

A number series follows a rule — differences, ratios, squares, cubes or two interleaved series — and asks for the next or missing term.

Key points

Arithmetic: constant difference (3, 7, 11, 15 → +4).
Geometric: constant ratio (2, 6, 18, 54 → × 3).
Second-difference series: differences themselves form a series (2, 6, 12, 20, 30 → +4, +6, +8, +10).
Mixed operations: × 2 + 1, × 3 − 1.
Alternate series: odd-position and even-position terms follow different rules.

Explanation

If differences grow fast, check multiplication or squares.
Factorial series: 1, 2, 6, 24, 120 (× 2, × 3, × 4, × 5).
n(n + 1): 2, 6, 12, 20, 30, 42.
Wrong-term questions: find the rule from most terms, then the one that breaks it.

Step by step

Write differences or ratios.
Identify the rule.
Compute and verify on earlier terms.

Examples

2, 6, 12, 20, 30, ? → differences 4, 6, 8, 10, 12 → 42.
1, 2, 6, 24, ? → × 2, × 3, × 4, × 5 → 120.
5, 11, 23, 47, ? → × 2 + 1 → 95.

Traps and advanced points

Trap: Stopping at first differences when second differences are needed.
Trap: Missing alternate-term patterns.
Trap: Ignoring a mixed × and + rule.

Quick revision

Differences, then ratios, then squares.
Check alternate terms.
Factorial: 1, 2, 6, 24, 120.

Practice MCQs

Find the next number: 4, 9, 16, 25, ?
1. 35
2. 49
3. 36
4. 30
Read chapter notes · Similar questions
Show answer
Answer: (c) 36. Ye squares hain: 2^2,3^2,4^2,5^2.
Find the next number: 1, 2, 6, 24, ?
1. 96
2. 72
3. 48
4. 120
Read chapter notes · Similar questions
Show answer
Answer: (d) 120. Pattern: ×2, ×3, ×4, …
Find the missing number: 3, 7, 15, 31, ?
1. 63
2. 55
3. 47
4. 62
Read chapter notes · Similar questions
Show answer
Answer: (a) 63. Pattern: ×2+1.
Find the next number: 2, 6, 12, 20, 30, ?
1. 40
2. 36
3. 44
4. 42
Read chapter notes · Similar questions
Show answer
Answer: (d) 42. Differences: 4,6,8,10 (increasing by 2).
Find the next number: 1, 4, 9, 16, 25, ?
1. 36
2. 30
3. 49
4. 35
Read chapter notes · Similar questions
Show answer
Answer: (a) 36. Perfect squares: 1^2 to 5^2.
Find the missing number: 5, 11, 23, 47, ?
1. 94
2. 93
3. 96
4. 95
Read chapter notes · Similar questions
Show answer
Answer: (d) 95. Pattern: ×2+1.
Find the next number: 2, 3, 5, 7, 11, ?
1. 13
2. 12
3. 15
4. 14
Read chapter notes · Similar questions
Show answer
Answer: (a) 13. Ye prime numbers ki series hai: 2,3,5,7,11.
Find the next number: 1, 8, 27, 64, ?
1. 81
2. 216
3. 125
4. 100
Read chapter notes · Similar questions
Show answer
Answer: (c) 125. Cubes: 1^3,2^3,3^3,4^3.
Find the missing number: 6, 11, 21, 36, 56, ?
1. 78
2. 81
3. 76
4. 80
Read chapter notes · Similar questions
Show answer
Answer: (b) 81. Differences: 5,10,15,20 (multiples of 5, increasing).
Find the odd term: 8, 27, 64, 100, 125
1. 100
2. 8
3. 64
4. 125
Read chapter notes · Similar questions
Show answer
Answer: (a) 100. 8,27,64,125 = perfect cubes (2^3,3^3,4^3,5^3).
Find the next number: 67, 72, 77, 82, 87, ?
1. 102
2. 92
3. 97
4. 87
Read chapter notes · Similar questions
Show answer
Answer: (b) 92. Constant difference = 5.
Find the next number: 54, 108, 216, 432, 864, ?
1. 1728
2. 2073.6
3. 1555.2
4. 1900.8
Read chapter notes · Similar questions
Show answer
Answer: (a) 1728. Each term ×2.
Find the next number: 101, 104, 107, 110, 113, ?
1. 113
2. 116
3. 122
4. 119
Read chapter notes · Similar questions
Show answer
Answer: (b) 116. Constant difference = 3.
Find the next term: 23, 27, 34, 38, 45, ?
1. 47
2. 51
3. 53
4. 49
Read chapter notes · Similar questions
Show answer
Answer: (d) 49. Differences alternate +4, +7.
Find the next term: 47, 50, 56, 59, 65, ?
1. 70
2. 68
3. 66
4. 72
Read chapter notes · Similar questions
Show answer
Answer: (b) 68. Differences alternate +3, +6.