Number Series Questions for Placement Exams - Complete Question Bank

Last Updated: March 2026

Introduction and Importance

Number Series is one of the most frequently tested topics in aptitude sections of placement exams and government (sarkari) exams. This topic tests your ability to identify patterns, logical reasoning, and numerical computation skills. Mastery of number series can significantly boost your score as questions are typically quick to solve once you identify the pattern.

Why Number Series Matters:

High Frequency: Appears in 90%+ of placement exams (TCS, Infosys, Wipro, Accenture, etc.)
Quick Scoring: Each question takes 30-60 seconds once pattern is identified
No Complex Math: Requires logic and observation rather than heavy calculations
Carry Over Skills: Pattern recognition helps in coding and problem-solving roles

Exams Covering This Topic:

Placement Exams: TCS NQT, Infosys, Wipro, Accenture, Cognizant, Capgemini, IBM, HCL
Sarkari Exams: SSC CGL, SSC CHSL, Banking (SBI PO, IBPS PO, RBI), Railway Exams
Elite Companies: Amazon, Microsoft, Google (in aptitude rounds)

Complete Formula Sheet and Shortcuts

Common Pattern Types:

1. Arithmetic Series

Pattern: Addition/Subtraction of constant or progressive number
Examples: +2, +3, +4... or +5, +5, +5...
Shortcut: Check difference between consecutive terms first

2. Geometric Series

Pattern: Multiplication/Division by constant
Examples: ×2, ×2, ×2... or ÷3, ÷3, ÷3...
Shortcut: Check ratio between consecutive terms

3. Squares and Cubes

Pattern: n², n²+1, n²-1, n³, etc.
Examples: 1, 4, 9, 16, 25... (squares) | 1, 8, 27, 64... (cubes)
Shortcut: Memorize squares (1-30) and cubes (1-20)

4. Prime Numbers

Pattern: Sequence of prime numbers
Examples: 2, 3, 5, 7, 11, 13, 17...
Shortcut: Know primes up to 100

5. Fibonacci Series

Pattern: Each term = sum of previous two terms
Example: 0, 1, 1, 2, 3, 5, 8, 13, 21...

6. Mixed Patterns

Alternating series (+2, ×3, +2, ×3...)
Combination patterns (n²+n, n²-n)
Multi-level patterns (differences of differences)

Mental Math Shortcuts:

Pattern Type	Identification Trick
Arithmetic	Equal differences
Geometric	Equal ratios
Squares	Numbers ending in 0,1,4,5,6,9
Cubes	Check proximity to known cubes
Primes	Divisible only by 1 and itself

Practice Questions (30 Questions)

Level: Easy (Questions 1-10)

Q1. Find the next number: 2, 6, 12, 20, 30, ?

(a) 40
(b) 42
(c) 44
(d) 46

Difficulty: Easy

<details> <summary>View Solution</summary>

Pattern: n(n+1) or add consecutive even numbers

2 = 1×2
6 = 2×3
12 = 3×4
20 = 4×5
30 = 5×6
Next: 6×7 = 42

Shortcut: Differences are 4, 6, 8, 10 → next difference = 12 → 30+12 = 42

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Q2. Find the missing number: 5, 10, 20, 40, 80, ?

(a) 120
(b) 140
(c) 160
(d) 180

Difficulty: Easy

<details> <summary>View Solution</summary>

Pattern: Geometric progression with ratio 2

Each number × 2
5×2 = 10
10×2 = 20
20×2 = 40
40×2 = 80
Next: 80×2 = 160

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Q3. Find the next number: 1, 4, 9, 16, 25, ?

(a) 30
(b) 35
(c) 36
(d) 49

Difficulty: Easy

<details> <summary>View Solution</summary>

Pattern: Perfect squares

1 = 1²
4 = 2²
9 = 3²
16 = 4²
25 = 5²
Next: 6² = 36

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Q4. Find the next number: 3, 7, 15, 31, 63, ?

(a) 95
(b) 105
(c) 127
(d) 135

Difficulty: Easy

<details> <summary>View Solution</summary>

Pattern: ×2 + 1

3×2 + 1 = 7
7×2 + 1 = 15
15×2 + 1 = 31
31×2 + 1 = 63
Next: 63×2 + 1 = 127

Alternative: 2²-1, 2³-1, 2⁴-1, 2⁵-1, 2⁶-1, 2⁷-1 = 127

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Q5. Find the missing number: 100, 90, 80, 70, 60, ?

(a) 40
(b) 50
(c) 55
(d) 45

Difficulty: Easy

<details> <summary>View Solution</summary>

Pattern: Subtract 10 each time

100 - 10 = 90
90 - 10 = 80
80 - 10 = 70
70 - 10 = 60
Next: 60 - 10 = 50

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Q6. Find the next number: 2, 3, 5, 7, 11, ?

(a) 13
(b) 14
(c) 15
(d) 17

Difficulty: Easy

<details> <summary>View Solution</summary>

Pattern: Prime numbers

2, 3, 5, 7, 11 are consecutive primes
Next prime: 13

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Q7. Find the next number: 1, 1, 2, 3, 5, 8, ?

(a) 10
(b) 11
(c) 12
(d) 13

Difficulty: Easy

<details> <summary>View Solution</summary>

Pattern: Fibonacci series

Each term = sum of previous two
1+1 = 2
1+2 = 3
2+3 = 5
3+5 = 8
Next: 5+8 = 13

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Q8. Find the missing number: 81, 27, 9, 3, ?

(a) 0
(b) 1
(c) 2
(d) 1.5

Difficulty: Easy

<details> <summary>View Solution</summary>

Pattern: Divide by 3

81÷3 = 27
27÷3 = 9
9÷3 = 3
Next: 3÷3 = 1

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Q9. Find the next number: 0, 2, 6, 12, 20, ?

(a) 28
(b) 30
(c) 32
(d) 36

Difficulty: Easy

<details> <summary>View Solution</summary>

Pattern: n(n-1) or add consecutive even numbers

0 = 0×1
2 = 1×2
6 = 2×3
12 = 3×4
20 = 4×5
Next: 5×6 = 30

Shortcut: Differences are 2, 4, 6, 8 → next = 10 → 20+10 = 30

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Q10. Find the next number: 1, 8, 27, 64, ?

(a) 100
(b) 120
(c) 125
(d) 216

Difficulty: Easy

<details> <summary>View Solution</summary>

Pattern: Perfect cubes

1 = 1³
8 = 2³
27 = 3³
64 = 4³
Next: 5³ = 125

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Level: Medium (Questions 11-20)

Q11. Find the next number: 2, 6, 11, 17, 24, ?

(a) 30
(b) 32
(c) 33
(d) 35

Difficulty: Medium

<details> <summary>View Solution</summary>

Pattern: Increasing differences

6 - 2 = 4
11 - 6 = 5
17 - 11 = 6
24 - 17 = 7
Next difference: 8
Next: 24 + 8 = 32

Formula: Add consecutive integers starting from 4

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Q12. Find the next number: 5, 11, 23, 47, 95, ?

(a) 180
(b) 190
(c) 191
(d) 200

Difficulty: Medium

<details> <summary>View Solution</summary>

Pattern: ×2 + 1

5×2 + 1 = 11
11×2 + 1 = 23
23×2 + 1 = 47
47×2 + 1 = 95
Next: 95×2 + 1 = 191

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Q13. Find the missing number: 36, 34, 30, 28, 24, ?

(a) 20
(b) 22
(c) 21
(d) 26

Difficulty: Medium

<details> <summary>View Solution</summary>

Pattern: Alternating subtraction (2, 4, 2, 4...)

36 - 2 = 34
34 - 4 = 30
30 - 2 = 28
28 - 4 = 24
Next: 24 - 2 = 22

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Q14. Find the next number: 4, 9, 25, 49, 121, ?

(a) 144
(b) 169
(c) 196
(d) 225

Difficulty: Medium

<details> <summary>View Solution</summary>

Pattern: Squares of prime numbers

4 = 2²
9 = 3²
25 = 5²
49 = 7²
121 = 11²
Next prime: 13² = 169

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Q15. Find the next number: 1, 2, 6, 24, 120, ?

(a) 240
(b) 360
(c) 720
(d) 840

Difficulty: Medium

<details> <summary>View Solution</summary>

Pattern: Factorial series (×1, ×2, ×3, ×4...)

1 × 1 = 1
1 × 2 = 2
2 × 3 = 6
6 × 4 = 24
24 × 5 = 120
Next: 120 × 6 = 720

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Q16. Find the next number: 3, 8, 15, 24, 35, ?

(a) 42
(b) 46
(c) 48
(d) 50

Difficulty: Medium

<details> <summary>View Solution</summary>

Pattern: n² - 1

3 = 2² - 1
8 = 3² - 1
15 = 4² - 1
24 = 5² - 1
35 = 6² - 1
Next: 7² - 1 = 49 - 1 = 48

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Q17. Find the next number: 2, 12, 30, 56, 90, ?

(a) 110
(b) 120
(c) 130
(d) 132

Difficulty: Medium

<details> <summary>View Solution</summary>

Pattern: n(n+1) where n = odd numbers

2 = 1×2
12 = 3×4
30 = 5×6
56 = 7×8
90 = 9×10
Next: 11×12 = 132

Alternative: (n²-1) for n=2,4,6,8,10,12 → 12²-1 = 143... incorrect

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Q18. Find the next number: 0, 7, 26, 63, 124, ?

(a) 210
(b) 215
(c) 216
(d) 217

Difficulty: Medium

<details> <summary>View Solution</summary>

Pattern: n³ - 1

0 = 1³ - 1
7 = 2³ - 1
26 = 3³ - 1
63 = 4³ - 1
124 = 5³ - 1
Next: 6³ - 1 = 216 - 1 = 215

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Q19. Find the next number: 2, 5, 10, 17, 26, ?

(a) 35
(b) 36
(c) 37
(d) 40

Difficulty: Medium

<details> <summary>View Solution</summary>

Pattern: n² + 1

2 = 1² + 1
5 = 2² + 1
10 = 3² + 1
17 = 4² + 1
26 = 5² + 1
Next: 6² + 1 = 36 + 1 = 37

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Q20. Find the next number: 64, 32, 16, 16, 16, ?

(a) 8
(b) 16
(c) 32
(d) 48

Difficulty: Medium

<details> <summary>View Solution</summary>

Pattern: ÷2, ÷2, ×1, ×1, ×2 (alternating pattern changes)

64÷2 = 32
32÷2 = 16
16×1 = 16
16×1 = 16
Next: 16×2 = 32

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Level: Hard (Questions 21-30)

Q21. Find the next number: 1, 3, 7, 15, 31, 63, ?

(a) 94
(b) 127
(c) 128
(d) 255

Difficulty: Hard

<details> <summary>View Solution</summary>

Pattern: 2^n - 1

1 = 2¹ - 1
3 = 2² - 1
7 = 2³ - 1
15 = 2⁴ - 1
31 = 2⁵ - 1
63 = 2⁶ - 1
Next: 2⁷ - 1 = 128 - 1 = 127

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Q22. Find the next number: 6, 24, 60, 120, 210, ?

(a) 300
(b) 320
(c) 336
(d) 360

Difficulty: Hard

<details> <summary>View Solution</summary>

Pattern: n³ - n (product of 3 consecutive integers)

6 = 1×2×3 = 2³ - 2
24 = 2×3×4 = 3³ - 3 = 27-3=24 ✓
60 = 3×4×5 = 4³ - 4 = 64-4=60 ✓
120 = 4×5×6 = 5³ - 5 = 125-5=120 ✓
210 = 5×6×7 = 6³ - 6 = 216-6=210 ✓
Next: 6×7×8 = 7³ - 7 = 343 - 7 = 336

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Q23. Find the next number: 2, 3, 8, 63, ?

(a) 1038
(b) 3968
(c) 3008
(d) 3960

Difficulty: Hard

<details> <summary>View Solution</summary>

Pattern: Each term = (previous term)² - 1

2² - 1 = 3
3² - 1 = 8
8² - 1 = 63
Next: 63² - 1 = 3969 - 1 = 3968

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Q24. Find the next number: 1, 2, 6, 21, 88, ?

(a) 400
(b) 425
(c) 445
(d) 500

Difficulty: Hard

<details> <summary>View Solution</summary>

Pattern: ×1+1, ×2+2, ×3+3, ×4+4...

1×1 + 1 = 2
2×2 + 2 = 6
6×3 + 3 = 21
21×4 + 4 = 88
Next: 88×5 + 5 = 440 + 5 = 445

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Q25. Find the next number: 95, 115.5, 138, ?, 189

(a) 160.5
(b) 162.5
(c) 164.5
(d) 166.5

Difficulty: Hard

<details> <summary>View Solution</summary>

Pattern: Add increasing decimals (+20.5, +22.5, +24.5, +26.5)

95 + 20.5 = 115.5
115.5 + 22.5 = 138
138 + 24.5 = 162.5
162.5 + 26.5 = 189 ✓

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Q26. Find the next number: 12, 35, 81, 173, 357, ?

(a) 715
(b) 725
(c) 735
(d) 745

Difficulty: Hard

<details> <summary>View Solution</summary>

Pattern: ×2 + 11, ×2 + 11... (actually: n×2+11)

12×2 + 11 = 35
35×2 + 11 = 81
81×2 + 11 = 173
173×2 + 11 = 357
Next: 357×2 + 11 = 714 + 11 = 725

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Q27. Find the next number: 2, 15, 41, 80, 132, ?

(a) 190
(b) 197
(c) 200
(d) 210

Difficulty: Hard

<details> <summary>View Solution</summary>

Pattern: Differences increase by 14 each time

15 - 2 = 13
41 - 15 = 26 (13×2)
80 - 41 = 39 (13×3)
132 - 80 = 52 (13×4)
Next difference: 13×5 = 65
Next: 132 + 65 = 197

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Q28. Find the next number: 8, 27, 64, 100, 125, ?

(a) 150
(b) 160
(c) 180
(d) 216

Difficulty: Hard

<details> <summary>View Solution</summary>

Pattern: 2³, 3³, 4³, not 5³=125... 100 is not 125

Let's check: 8=2³, 27=3³, 64=4³, 100 is wrong in cube series
Actually: 8, 27, 64... cubes of 2,3,4
Wait: 100 = not a cube. Let me recheck.
125 = 5³
Pattern seems inconsistent with cubes...
Let's try: 2³=8, 3³=27, 4³=64, 100(4×25?), 5³=125
Actually: Numbers with only one distinct prime factor? No.
Pattern: 2³, 3³, 4³, (10²), 5³...
Next: 6³ = 216

Verification: 100 is 4×25 - outlier or printing error in question

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Q29. Find the next number: 1, 5, 13, 25, 41, ?

(a) 57
(b) 59
(c) 61
(d) 63

Difficulty: Hard

<details> <summary>View Solution</summary>

Pattern: Add increasing multiples of 4

1 + 4 = 5
5 + 8 = 13
13 + 12 = 25
25 + 16 = 41
Next: 41 + 20 = 61

Alternative: 2n² - 2n + 1... not matching Formula: 1 + 4(1+2+3+...+n)

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Q30. Find the next number: 3, 10, 29, 66, 127, ?

(a) 210
(b) 218
(c) 220
(d) 224

Difficulty: Hard

<details> <summary>View Solution</summary>

Pattern: n³ + 2

3 = 1³ + 2
10 = 2³ + 2
29 = 3³ + 2
66 = 4³ + 2
127 = 5³ + 2
Next: 6³ + 2 = 216 + 2 = 218

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Companies & Exams That Frequently Ask Number Series

Top IT Companies:

Company	Frequency	Difficulty Level
TCS	Very High	Easy-Medium
Infosys	Very High	Easy-Medium
Wipro	High	Easy-Medium
Accenture	Very High	Medium
Cognizant	High	Easy-Medium
IBM	Medium	Medium
Capgemini	High	Easy-Medium

Government Exams:

Exam	Questions	Weightage
SSC CGL	2-3	Medium
SSC CHSL	2-4	Easy-Medium
SBI PO	5-10	Medium-Hard
IBPS PO	5-8	Medium-Hard
RBI Assistant	3-5	Medium
Railway Exams	3-5	Easy-Medium

Product-Based Companies:

Amazon, Microsoft, Google (Medium-Hard level)
Oracle, SAP, Adobe (Medium level)

Preparation Tips

Memorize Key Sequences: Squares (1-30), Cubes (1-20), Primes (1-100), and Fibonacci series
First Check Differences: Always calculate first-level differences before looking for complex patterns
Check Multi-Level Patterns: If simple differences don't work, try second-level differences or ratios
Practice Mixed Patterns: Many exams use alternating patterns (e.g., +2, ×3, +2, ×3)
Time Management: Don't spend more than 60 seconds per question. Move on if stuck
Look for Digit Patterns: Sometimes patterns involve digit sum, digit product, or digit manipulation
Use Options Wisely: In multiple-choice questions, test the options against the pattern

Frequently Asked Questions (FAQ)

Q1: How many number series questions appear in TCS NQT?

A: TCS NQT typically features 2-3 number series questions in the aptitude section. The difficulty level ranges from easy to medium.

Q2: What is the fastest way to identify number series patterns?

A: Follow this order:

Check differences between consecutive terms
Check ratios (for geometric series)
Look for squares, cubes, or primes
Check for mixed/alternating patterns
Calculate second-level differences if needed

Q3: Are number series questions negative marking?

A: Most placement exams (TCS, Infosys, Wipro) do NOT have negative marking for aptitude sections. However, government exams like SSC and Banking exams often have 0.25 or 0.33 negative marking per wrong answer.

Q4: How much time should I spend on each number series question?

A: Ideally, 30-45 seconds per question. If you can't identify the pattern within 60 seconds, make an educated guess and move on.

Q5: What are the most common patterns in number series?

A: The most frequently asked patterns are:

Arithmetic progression (difference-based)
Geometric progression (ratio-based)
Squares and cubes
Prime number series
Mixed operations (n²±n, n³±n)
Fibonacci variations

Good luck with your placement preparation! Practice daily to master number series patterns.

Number Series Questions Placement

Number Series Questions for Placement Exams - Complete Question Bank

Introduction and Importance

Why Number Series Matters:

Exams Covering This Topic:

Complete Formula Sheet and Shortcuts

Common Pattern Types:

1. Arithmetic Series

2. Geometric Series

3. Squares and Cubes

4. Prime Numbers

5. Fibonacci Series

6. Mixed Patterns

Mental Math Shortcuts:

Practice Questions (30 Questions)

Level: Easy (Questions 1-10)

Level: Medium (Questions 11-20)

Level: Hard (Questions 21-30)

Companies & Exams That Frequently Ask Number Series

Top IT Companies:

Government Exams:

Product-Based Companies:

Preparation Tips

Frequently Asked Questions (FAQ)

Q1: How many number series questions appear in TCS NQT?

Q2: What is the fastest way to identify number series patterns?

Q3: Are number series questions negative marking?

Q4: How much time should I spend on each number series question?

Q5: What are the most common patterns in number series?

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