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Number Series

Quantitative Aptitude / DI · Speed Calculation

Useful for: Railway RRB, IBPS Banking, KVS, NVS, OTET, UGC NET, EMRS, OSSC RHT — Regular High School Teacher

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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 term: 71, 73, 78, 80, 85, ?
1. 85
2. 91
3. 87
4. 89
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Answer: (c) 87. Differences alternate +2, +5.
Find the next term: 78, 82, 87, 91, 96, ?
1. 104
2. 98
3. 102
4. 100
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Answer: (d) 100. Differences alternate +4, +5.
Find the next term: 83, 87, 95, 99, 107, ?
1. 111
2. 115
3. 109
4. 113
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Answer: (a) 111. Differences alternate +4, +8.
Find the next term: 9, 16, 25, 36, 49, ?
1. 64
2. 79
3. 94
4. 49
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Answer: (a) 64. These are consecutive squares.
Find the next term: 96, 98, 104, 106, 112, ?
1. 112
2. 116
3. 118
4. 114
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Answer: (d) 114. Differences alternate +2, +6.
Find the next term: 1936, 2025, 2116, 2209, 2304, ?
1. 2498
2. 2595
3. 2401
4. 2304
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Answer: (c) 2401. These are consecutive squares.
Find the next number: 86, 92, 98, 104, 110, ?
1. 128
2. 116
3. 122
4. 110
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Answer: (b) 116. Constant difference = 6.
Find the next term: 26, 28, 34, 36, 42, ?
1. 44
2. 42
3. 46
4. 48
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Answer: (a) 44. Differences alternate +2, +6.
Find the next term: 53, 57, 68, 72, 83, ?
1. 85
2. 87
3. 91
4. 89
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Answer: (b) 87. Differences alternate +4, +11.
Find the next term: 39, 44, 55, 60, 71, ?
1. 80
2. 78
3. 74
4. 76
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Answer: (d) 76. Differences alternate +5, +11.
Find the next number: 58, 63, 68, 73, 78, ?
1. 93
2. 83
3. 78
4. 88
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Answer: (b) 83. Constant difference = 5.
Find the next number: 72, 144, 288, 576, 1152, ?
1. 2534.4
2. 2304
3. 2073.6
4. 2764.8
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Answer: (b) 2304. Each term ×2.
Find the next term: 100, 121, 144, 169, 196, ?
1. 283
2. 196
3. 254
4. 225
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Answer: (d) 225. These are consecutive squares.
Find the next number: 80, 89, 98, 107, 116, ?
1. 143
2. 116
3. 125
4. 134
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Answer: (c) 125. Constant difference = 9.
Find the next term: 4096, 4225, 4356, 4489, 4624, ?
1. 5035
2. 4898
3. 4761
4. 4624
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Answer: (c) 4761. These are consecutive squares.