Number Series Questions Placement
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...
What changed in 2026 drives
Mass-recruiter offer letters are flatter for 2026 batch - the 4-5 LPA ASE band has barely budged in three years while inflation eats real wages. Premium tracks (Digital, Pro, Elite, Specialist) are still where the differential lives, and they are entirely test-driven. If you are aiming higher than the default offer, the coding round is not optional pageantry - it is the entire interview.
What I'd actually study for this
- 01Two solid coding-round answers (1 medium-hard DSA each, with edge-case discussion) > five half-baked ones
- 02One real project you can defend end-to-end - file paths, design decisions, and what you would change
- 03One DBMS schema you actually built (not a textbook ER diagram), with at least 3 join-heavy queries written from memory
- 04Three behavioural STAR stories: failure recovered, conflict handled, ownership taken
Where most candidates trip up
The single biggest mistake is treating company-specific guides as primary prep and DSA as secondary. It is the opposite. Mass recruiters use the test as a filter, but premium tracks at every IT services company use coding to allocate offer band. Spend 70% of prep time on DSA + system fundamentals, 20% on company-specific patterns, 10% on HR rehearsal. Reverse that ratio and you collect the default offer.
Editorial commentary by Aditya Sharma · written for PapersAdda · not generated, not aggregated.
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
</details>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
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
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
</details>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
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
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
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
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
</details>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
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
</details>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
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
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
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
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
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
</details>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
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
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
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
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
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
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
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 ✓
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
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
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
</details>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)
</details>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
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
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- Number Series For Placement
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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.
Operator's Read (2026-05-16 verification update)
After cross-referencing IndiaBix, PrepInsta, GeeksforGeeks, LeetCode, and 2025-2026 candidate reports on placement tests, here is the operator-level read on Number Series for the 2026 cycle.
Frequency signal. Number-Series problems appear in roughly 1 in 3 placement reasoning sections, often in find-the-next-term or find-the-wrong-term format.
Companies testing this topic. TCS, Wipro, Accenture, Cognizant, Infosys, Capgemini, HCL all test Number Series in reasoning sections.
Depth-bar signal. Per IndiaBix and PrepInsta 2025-2026 question banks, the standard difficulty involves arithmetic, geometric, alternating, and square-or-cube progressions.
My recommended approach. Compute differences between consecutive terms first. If differences are constant, arithmetic. If ratios are constant, geometric. If neither, check for square-or-cube patterns.
The single most common trap. Mixed-progression series (alternating arithmetic and geometric) are the dominant trap. Always check the second-level difference if the first-level pattern is not obvious.
Practice Schedule (7-Day Drill for Number Series)
Run this schedule one week before your placement test. Skipping any day shows up as a measurable weak signal in problem-solving speed.
- Day 1. Read the topic theory cold. Note the 4 to 5 core formulas or patterns.
- Day 2. Solve 10 easy problems with the textbook approach. Aim for accuracy over speed.
- Day 3. Solve 15 medium problems. Track time per problem. Target under 90 seconds per problem.
- Day 4. Solve 10 medium and 5 hard problems. Identify your weakest sub-pattern.
- Day 5. Drill only the weakest sub-pattern (15 problems). Goal is reflex on that pattern.
- Day 6. Take a full mock section with mixed problems. Score yourself against the target.
- Day 7. Rest, light revision only. Re-read your formula cheat-sheet once.
Verified Sources (May 2026)
Question patterns and frequency data referenced above are aggregated from these public sources. Cross-check question banks for your specific test format.
- IndiaBix Logical Reasoning question bank, accessed May 2026
- PrepInsta Number Series question bank, 2025-2026 placement cycle
- GeeksforGeeks Number Series tutorial and practice section
- LeetCode discuss interview-experience posts tagged Logical Reasoning, 2025 to May 2026
- AmbitionBox and Glassdoor 2025-2026 candidate interview reports for Number Series
Methodology applied to this articlelast verified 9 Jun 2026
- No fabricated salary numbers or success rates. If we quote a range, it's sourced.
- No noun-substituted templates. This article was not generated by swapping company names in a stock prompt.
- No paid placements, sponsored coaching links, or affiliate-shilled course pushes.
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