Number Series Solved Examples 2026 (45+ Problems with Solutions)

Last Updated: June 2026

This page collects 45+ solved number series problems at placement-exam difficulty, organized by pattern type: arithmetic, geometric, square and cube, mixed, and odd-one-out. Each problem has a full step-by-step solution. Candidates report number series as a fast-scoring reasoning topic in TCS, Infosys, and Wipro rounds once the common patterns are recognized on sight.

Pattern Reference

Section A: Arithmetic and Geometric (Problems 1-12)

Problem 1. 3, 8, 13, 18, ? Solution: Constant difference 5, next = 23.

Problem 2. 5, 10, 20, 40, ? Solution: Ratio 2, next = 80.

Problem 3. 7, 11, 15, 19, ? Solution: Difference 4, next = 23.

Problem 4. 2, 6, 18, 54, ? Solution: Ratio 3, next = 162.

Problem 5. 100, 90, 80, 70, ? Solution: Difference -10, next = 60.

Problem 6. 1, 3, 9, 27, ? Solution: Ratio 3, next = 81.

Problem 7. 12, 17, 22, 27, ? Solution: Difference 5, next = 32.

Problem 8. 64, 32, 16, 8, ? Solution: Ratio 1/2, next = 4.

Problem 9. 6, 13, 20, 27, ? Solution: Difference 7, next = 34.

Problem 10. 3, 12, 48, 192, ? Solution: Ratio 4, next = 768.

Problem 11. 50, 45, 40, 35, ? Solution: Difference -5, next = 30.

Problem 12. 2, 4, 8, 16, ? Solution: Ratio 2, next = 32.

Section B: Square and Cube (Problems 13-22)

Problem 13. 1, 4, 9, 16, ? Solution: Squares of 1, 2, 3, 4, next = 25.

Problem 14. 1, 8, 27, 64, ? Solution: Cubes of 1, 2, 3, 4, next = 125.

Problem 15. 4, 9, 16, 25, ? Solution: Squares of 2, 3, 4, 5, next = 36.

Problem 16. 8, 27, 64, 125, ? Solution: Cubes of 2, 3, 4, 5, next = 216.

Problem 17. 2, 5, 10, 17, ? Solution: n squared plus 1: 1+1, 4+1, 9+1, 16+1, next 25+1 = 26.

Problem 18. 0, 3, 8, 15, ? Solution: n squared minus 1: 1-1, 4-1, 9-1, 16-1, next 25-1 = 24.

Problem 19. 1, 4, 27, 256, ? Solution: n to the power n: 1, 2 squared, 3 cubed, 4 to fourth, next 5 to fifth = 3125.

Problem 20. 121, 144, 169, 196, ? Solution: Squares of 11, 12, 13, 14, next = 225.

Problem 21. 2, 9, 28, 65, ? Solution: n cubed plus 1: 1+1, 8+1, 27+1, 64+1, next 125+1 = 126.

Problem 22. 3, 6, 11, 18, ? Solution: n squared plus 2: 1+2, 4+2, 9+2, 16+2, next 25+2 = 27.

Section C: Mixed and Special (Problems 23-34)

Problem 23. 5, 11, 23, 47, ? Solution: Previous times 2 plus 1, next = 95.

Problem 24. 2, 5, 11, 23, ? Solution: Previous times 2 plus 1, next = 47.

Problem 25. 1, 1, 2, 3, 5, 8, ? Solution: Fibonacci, next = 13.

Problem 26. 1, 2, 6, 24, 120, ? Solution: Factorials, next = 720.

Problem 27. 2, 6, 12, 20, 30, ? Solution: n(n+1): 1×2, 2×3, 3×4, 4×5, 5×6, next 6×7 = 42.

Problem 28. 1, 3, 6, 10, 15, ? Solution: Triangular numbers, differences 2, 3, 4, 5, next = 21.

Problem 29. 6, 11, 21, 41, 81, ? Solution: Previous times 2 minus 1, next = 161.

Problem 30. 3, 7, 16, 35, 74, ? Solution: Previous times 2 plus growing add: 3×2+1, 7×2+2, 16×2+3, 35×2+4, next 74×2+5 = 153.

Problem 31. 1, 10, 2, 20, 3, ? Solution: Alternating series, odd positions 1,2,3 and even positions 10,20, next even = 30.

Problem 32. 4, 8, 16, 32, ? Solution: Ratio 2, next = 64.

Problem 33. 2, 3, 5, 7, 11, ? Solution: Prime numbers, next = 13.

Problem 34. 1, 4, 10, 22, 46, ? Solution: Previous times 2 plus 2, next = 94.

Section D: Odd One Out (Problems 35-45)

Problem 35. 8, 27, 64, 100, 125. Odd one out? Solution: All are cubes except 100; answer 100.

Problem 36. 4, 9, 16, 25, 30, 36. Odd one out? Solution: All are squares except 30; answer 30.

Problem 37. 2, 3, 5, 7, 9, 11. Odd one out? Solution: All prime except 9; answer 9.

Problem 38. 121, 144, 169, 180, 196. Odd one out? Solution: All squares except 180; answer 180.

Problem 39. 3, 5, 7, 12, 13. Odd one out? Solution: All prime except 12; answer 12.

Problem 40. 1, 8, 27, 49, 64. Odd one out? Solution: Cubes except 49 which is a square; answer 49.

Problem 41. 10, 20, 30, 45, 50. Odd one out? Solution: All multiples of 10 except 45; answer 45.

Problem 42. 16, 25, 36, 49, 60. Odd one out? Solution: All squares except 60; answer 60.

Problem 43. 2, 4, 6, 8, 9, 10. Odd one out? Solution: All even except 9; answer 9.

Problem 44. 5, 10, 15, 22, 25. Odd one out? Solution: All multiples of 5 except 22; answer 22.

Problem 45. 1, 4, 9, 16, 20, 25. Odd one out? Solution: All squares except 20; answer 20.

How To Read A Series In Under Ten Seconds

The reason strong candidates solve number series almost instantly is that they run a fixed checklist rather than staring at the numbers hoping a pattern appears. The checklist has a strict order, and each step rules out a family of patterns before moving on.

The first move is always to compute the differences between consecutive terms. If those differences are equal, the series is arithmetic and you are done. If the differences themselves form a recognizable sequence, such as 2, 4, 6 or 1, 3, 5, the series is built on a growing difference and you extend that inner sequence. If the differences are not helpful, the second move is to check the ratio between consecutive terms; a constant ratio means a geometric series. The third move is to test whether the terms are squares, cubes, or one more or one less than a square or cube, since these decorated power series are extremely common in placement tests. The fourth move is to test the previous-term-times-two-plus-or-minus-a-constant rule, which generates sequences like 5, 11, 23, 47 that look irregular but follow a simple recursive rule. The final move, used only when all else fails, is to suspect an alternating series where two independent sequences are interleaved; split the terms into odd and even positions and analyze each separately.

Running this checklist in order means you almost never get stuck, because each step eliminates a whole class of possibilities. Candidates report that the discipline of always starting with differences, rather than guessing, is what makes the difference between a confident ten-second solve and a thirty-second flounder.

Common Traps In Number Series

A handful of traps account for most wrong answers in this topic. The first is stopping at the first pattern that seems to fit without checking it against every term; a rule that explains three of four terms is not the rule. The second is confusing a growing-difference series with a geometric one, since both accelerate; the test is whether the gap between terms is added (growing difference) or multiplied (geometric). The third is missing a decorated power series, such as 2, 5, 10, 17, where each term is a perfect square plus one; if raw differences look like 3, 5, 7 you should immediately suspect squares. The fourth is failing to spot an alternating series because you analyze all terms together instead of splitting odd and even positions. Awareness of these four traps, combined with the ordered checklist above, resolves the vast majority of placement number-series questions.

Key Takeaways

Candidates report that the fastest way to crack a number series is to compute the differences first, since arithmetic and growing-difference patterns cover the majority of questions. If differences fail, the ratio, square, cube, and times-two-plus-one tests resolve almost everything else.

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Frequently Asked Questions

How do I approach an unknown number series?

First check the differences between consecutive terms. If the differences are constant it is arithmetic; if they grow in a pattern, look at the second differences. If terms multiply by a constant it is geometric. If neither, test squares, cubes, primes, or an alternating two-series pattern. Candidates report that checking differences first solves most series quickly.

What are the most common number series patterns?

The high-frequency patterns are arithmetic (constant difference), geometric (constant ratio), square and cube sequences, prime sequences, Fibonacci-style sums, and the previous-term times two plus or minus one pattern. Recognizing these on sight is the fastest route to a correct answer under time pressure.

How do I solve odd-one-out series questions?

Identify the rule that fits all but one term. Often the series is squares, cubes, or primes with a single intruder. Test each candidate against the rule and the one that breaks it is the answer. Candidates report that squares and cubes with one non-matching value are the most common odd-one-out format.