InterviewSam
Log inStart free

Number Series

Find the next or wrong number in a series.

45 solved questions · 15 easy · 20 medium · 10 hard

Take a 10-question quiz on Number Series, no login

Shortcuts & formulas

  • Check first the differences between consecutive terms: constant (AP), increasing by a fixed amount (second-order), or doubling (+2, +4, +8...).
  • If the ratios are constant it is a GP; ratios 1, 2, 3, 4... suggest factorial-type series (×1, ×2, ×3...).
  • Learn squares up to 30 and cubes up to 15: series like n² ± k and n³ ± n are very common.
  • Pattern 'multiply by a and add b' (for example ×2 + 1: 3, 7, 15, 31) shows up often; test it when differences keep growing.
  • Two interleaved series: split odd-position and even-position terms and examine each separately.
  • Wrong-number series: find the rule from the terms that agree, then see which term breaks it. Check the neighbours of the wrong term too.
  • Prime series: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37 ... Triangular numbers: 1, 3, 6, 10, 15, 21, 28.

Solved examples

Try each one first, then open the answer and the step-by-step solution.

Easy questions

Q1.

Find the next number in the series: 5, 9, 13, 17, ?

  1. A21
  2. B20
  3. C22
  4. D25
Show answer & solution

Answer: A. 21

Solution

Each term is 4 more than the previous (+4). 17 + 4 = 21 Answer: 21

Q2.

Find the next number in the series: 100, 93, 86, 79, ?

  1. A71
  2. B72
  3. C73
  4. D70
Show answer & solution

Answer: B. 72

Solution

Each term is 7 less than the previous (-7). 79 - 7 = 72 Answer: 72

Q3.

Find the next number in the series: 3, 6, 12, 24, ?

  1. A36
  2. B42
  3. C48
  4. D50
Show answer & solution

Answer: C. 48

Solution

Each term is double the previous (×2). 24 × 2 = 48 Answer: 48

Q4.

Find the next number in the series: 1, 4, 9, 16, 25, ?

  1. A30
  2. B35
  3. C49
  4. D36
Show answer & solution

Answer: D. 36

Solution

Perfect squares: 1², 2², 3², 4², 5², next 6². 6² = 36 Answer: 36

Q5.

Find the next number in the series: 1, 8, 27, 64, ?

  1. A125
  2. B100
  3. C81
  4. D128
Show answer & solution

Answer: A. 125

Solution

Perfect cubes: 1³, 2³, 3³, 4³, next 5³. 5³ = 125 Answer: 125

Q6.

Find the next number in the series: 2, 6, 18, 54, ?

  1. A108
  2. B162
  3. C160
  4. D135
Show answer & solution

Answer: B. 162

Solution

Each term is 3 times the previous (×3). 54 × 3 = 162 Answer: 162

Q7.

Find the next number in the series: 2, 3, 5, 7, 11, ?

  1. A12
  2. B14
  3. C13
  4. D15
Show answer & solution

Answer: C. 13

Solution

These are consecutive prime numbers: 2, 3, 5, 7, 11, next prime after 11 is 13. Answer: 13

Q8.

Find the next number in the series: 1, 3, 6, 10, 15, ?

  1. A20
  2. B22
  3. C25
  4. D21
Show answer & solution

Answer: D. 21

Solution

Differences: 2, 3, 4, 5 (increase by 1 each time) - triangular numbers. Next difference = 6, so 15 + 6 = 21 Answer: 21

Q9.

Find the next number in the series: 2, 5, 10, 17, 26, ?

  1. A37
  2. B36
  3. C38
  4. D35
Show answer & solution

Answer: A. 37

Solution

Terms are n² + 1: 1²+1, 2²+1, 3²+1, 4²+1, 5²+1, next 6² + 1 = 37 Answer: 37

Q10.

Find the next number in the series: 3, 7, 15, 31, ?

  1. A64
  2. B63
  3. C62
  4. D65
Show answer & solution

Answer: B. 63

Solution

Each term = previous × 2 + 1 (3×2+1 = 7, 7×2+1 = 15, 15×2+1 = 31). Next = 31 × 2 + 1 = 63 Answer: 63

Q11.

Find the next number in the series: 2, 3, 5, 8, 12, ?

  1. A16
  2. B18
  3. C17
  4. D15
Show answer & solution

Answer: C. 17

Solution

Differences are 1, 2, 3, 4 (growing by 1). Next difference = 5, so 12 + 5 = 17 Answer: 17

Q12.

Find the next number in the series: 64, 32, 16, 8, ?

  1. A2
  2. B3
  3. C6
  4. D4
Show answer & solution

Answer: D. 4

Solution

Each term is half the previous (÷2). 8 ÷ 2 = 4 Answer: 4

Q13.

Find the next number in the series: 7, 14, 21, 28, ?

  1. A35
  2. B34
  3. C36
  4. D42
Show answer & solution

Answer: A. 35

Solution

Multiples of 7: 7×1, 7×2, 7×3, 7×4, next 7×5 = 35 Answer: 35

Q14.

Find the next number in the series: 1, 1, 2, 3, 5, 8, ?

  1. A11
  2. B13
  3. C12
  4. D16
Show answer & solution

Answer: B. 13

Solution

Each term is the sum of the previous two (Fibonacci). 5 + 8 = 13 Answer: 13

Q15.

Find the next number in the series: 1, 2, 4, 7, 11, 16, ?

  1. A21
  2. B23
  3. C22
  4. D20
Show answer & solution

Answer: C. 22

Solution

Differences: 1, 2, 3, 4, 5 (growing by 1). Next difference = 6, so 16 + 6 = 22 Answer: 22

Medium questions

Q16.

Find the next number in the series: 2, 10, 30, 68, 130, ?

  1. A216
  2. B220
  3. C226
  4. D222
Show answer & solution

Answer: D. 222

Solution

Terms are n³ + n: 1+1=2, 8+2=10, 27+3=30, 64+4=68, 125+5=130. Next: 6³ + 6 = 216 + 6 = 222 Answer: 222

Q17.

Find the next number in the series: 16, 24, 36, 54, ?

  1. A81
  2. B72
  3. C80
  4. D90
Show answer & solution

Answer: A. 81

Solution

Each term is 1.5 times the previous (×3/2). 16→24→36→54 54 × 1.5 = 81 Answer: 81

Q18.

Find the next number in the series: 5, 9, 17, 33, 65, ?

  1. A130
  2. B129
  3. C127
  4. D131
Show answer & solution

Answer: B. 129

Solution

Each term = previous × 2 - 1 (5×2-1 = 9, 9×2-1 = 17, 17×2-1 = 33, 33×2-1 = 65). Next = 65 × 2 - 1 = 129 Answer: 129

Q19.

Find the next number in the series: 1, 2, 6, 24, 120, ?

  1. A600
  2. B240
  3. C720
  4. D840
Show answer & solution

Answer: C. 720

Solution

Multipliers: ×2, ×3, ×4, ×5 (factorials 1!, 2!, 3!, 4!, 5!). Next multiplier ×6: 120 × 6 = 720 Answer: 720

Q20.

Find the next number in the series: 2, 3, 5, 9, 17, 33, ?

  1. A49
  2. B64
  3. C66
  4. D65
Show answer & solution

Answer: D. 65

Solution

Differences: 1, 2, 4, 8, 16 (doubling). Next difference = 32, so 33 + 32 = 65 Answer: 65

Q21.

Find the next number in the series: 3, 10, 6, 20, 12, 40, ?

  1. A24
  2. B48
  3. C36
  4. D30
Show answer & solution

Answer: A. 24

Solution

Two interleaved series. Odd positions: 3, 6, 12, (24) - each ×2. Even positions: 10, 20, 40 - each ×2. The missing term is in an odd position: 12 × 2 = 24 Answer: 24

Q22.

Find the next number in the series: 0, 3, 8, 15, 24, ?

  1. A34
  2. B35
  3. C36
  4. D32
Show answer & solution

Answer: B. 35

Solution

Terms are n² - 1 for n = 1..5: 0, 3, 8, 15, 24. Next: 6² - 1 = 35 Answer: 35

Q23.

Find the next number in the series: 2, 4, 12, 48, 240, ?

  1. A720
  2. B1200
  3. C1440
  4. D960
Show answer & solution

Answer: C. 1440

Solution

Multipliers: ×2, ×3, ×4, ×5, so next ×6. 240 × 6 = 1440 Answer: 1440

Q24.

Find the next number in the series: 11, 13, 17, 19, 23, ?

  1. A27
  2. B31
  3. C25
  4. D29
Show answer & solution

Answer: D. 29

Solution

Consecutive prime numbers: 11, 13, 17, 19, 23, next prime is 29. Answer: 29

Q25.

Find the next number in the series: 120, 99, 80, 63, 48, ?

  1. A35
  2. B36
  3. C33
  4. D32
Show answer & solution

Answer: A. 35

Solution

Terms are n² - 1 going down: 11²-1 = 120, 10²-1 = 99, 9²-1 = 80, 8²-1 = 63, 7²-1 = 48. Next: 6² - 1 = 35 (differences 21, 19, 17, 15, 13) Answer: 35

Q26.

Find the next number in the series: 7, 9, 13, 21, 37, ?

  1. A53
  2. B69
  3. C61
  4. D67
Show answer & solution

Answer: B. 69

Solution

Differences: 2, 4, 8, 16 (doubling). Next difference = 32, so 37 + 32 = 69 Answer: 69

Q27.

Find the next number in the series: 1, 4, 27, 256, ?

  1. A1024
  2. B625
  3. C3125
  4. D2500
Show answer & solution

Answer: C. 3125

Solution

Terms are n^n: 1¹, 2², 3³, 4⁴, next 5⁵. 5⁵ = 3125 Answer: 3125

Q28.

Find the wrong number in the series: 4, 9, 14, 19, 25, 29, 34

  1. A9
  2. B14
  3. C34
  4. D25
Show answer & solution

Answer: D. 25

Solution

Rule: +5 each time (4, 9, 14, 19, 24, 29, 34). 19 + 5 = 24, not 25. Answer: 25

Q29.

Find the wrong number in the series: 2, 6, 18, 54, 160, 486

  1. A160
  2. B6
  3. C18
  4. D486
Show answer & solution

Answer: A. 160

Solution

Rule: ×3 each time (2, 6, 18, 54, 162, 486). 54 × 3 = 162, not 160. Answer: 160

Q30.

Find the wrong number in the series: 1, 4, 9, 16, 24, 36, 49

  1. A4
  2. B24
  3. C9
  4. D49
Show answer & solution

Answer: B. 24

Solution

Perfect squares 1, 4, 9, 16, 25, 36, 49. The fifth term should be 25, not 24. Answer: 24

Q31.

Find the wrong number in the series: 3, 7, 15, 31, 64, 127

  1. A7
  2. B15
  3. C64
  4. D127
Show answer & solution

Answer: C. 64

Solution

Rule: ×2 + 1 (3, 7, 15, 31, 63, 127). 31 × 2 + 1 = 63, not 64. Answer: 64

Q32.

Find the wrong number in the series: 5, 6, 8, 11, 15, 21, 26

  1. A6
  2. B8
  3. C26
  4. D21
Show answer & solution

Answer: D. 21

Solution

Differences should be 1, 2, 3, 4, 5, 6: 5, 6, 8, 11, 15, 20, 26. 15 + 5 = 20, not 21. Answer: 21

Q33.

Find the wrong number in the series: 2, 5, 10, 17, 26, 37, 48

  1. A48
  2. B5
  3. C10
  4. D37
Show answer & solution

Answer: A. 48

Solution

Terms are n² + 1: 2, 5, 10, 17, 26, 37, 50. 7² + 1 = 50, not 48. Answer: 48

Q34.

Find the wrong number in the series: 1, 2, 6, 24, 100, 720

  1. A2
  2. B100
  3. C6
  4. D720
Show answer & solution

Answer: B. 100

Solution

Multipliers should be ×2, ×3, ×4, ×5, ×6: 1, 2, 6, 24, 120, 720. 24 × 5 = 120, not 100. Answer: 100

Q35.

Find the wrong number in the series: 10, 11, 14, 19, 26, 36, 46

  1. A11
  2. B14
  3. C36
  4. D46
Show answer & solution

Answer: C. 36

Solution

Differences should be 1, 3, 5, 7, 9, 11: 10, 11, 14, 19, 26, 35, 46. 26 + 9 = 35, not 36. Answer: 36

Hard questions

Q36.

Find the next number in the series: 2, 12, 36, 80, 150, ?

  1. A216
  2. B210
  3. C264
  4. D252
Show answer & solution

Answer: D. 252

Solution

Terms are n² × (n + 1): 1²×2 = 2, 2²×3 = 12, 3²×4 = 36, 4²×5 = 80, 5²×6 = 150. Next: 6² × 7 = 252 Answer: 252

Q37.

Find the next number in the series: 6, 11, 21, 36, 56, ?

  1. A81
  2. B76
  3. C86
  4. D84
Show answer & solution

Answer: A. 81

Solution

Differences: 5, 10, 15, 20 (multiples of 5). Next difference = 25, so 56 + 25 = 81 Answer: 81

Q38.

Find the next number in the series: 4, 5, 12, 39, 160, ?

  1. A800
  2. B805
  3. C645
  4. D810
Show answer & solution

Answer: B. 805

Solution

Rule: ×1 + 1, ×2 + 2, ×3 + 3, ×4 + 4, ... 4×1+1 = 5, 5×2+2 = 12, 12×3+3 = 39, 39×4+4 = 160 Next: 160 × 5 + 5 = 805 Answer: 805

Q39.

Find the next number in the series: 1, 2, 6, 15, 31, 56, ?

  1. A81
  2. B90
  3. C92
  4. D96
Show answer & solution

Answer: C. 92

Solution

Differences: 1², 2², 3², 4², 5² = 1, 4, 9, 16, 25 Series: 1, 2 (+1), 6 (+4), 15 (+9), 31 (+16), 56 (+25). Next difference 6² = 36, so 56 + 36 = 92 Answer: 92

Q40.

Find the next number in the series: 3, 8, 6, 16, 12, 32, 24, ?

  1. A48
  2. B56
  3. C36
  4. D64
Show answer & solution

Answer: D. 64

Solution

Two interleaved series. Odd positions: 3, 6, 12, 24 (×2). Even positions: 8, 16, 32, (64) (×2). The next term is in an even position: 32 × 2 = 64 Answer: 64

Q41.

Find the next number in the series: 0, 6, 24, 60, 120, 210, ?

  1. A336
  2. B330
  3. C343
  4. D342
Show answer & solution

Answer: A. 336

Solution

Terms are n³ - n: 1-1=0, 8-2=6, 27-3=24, 64-4=60, 125-5=120, 216-6=210. Next: 7³ - 7 = 343 - 7 = 336 Answer: 336

Q42.

Find the wrong number in the series: 2, 5, 11, 23, 46, 95

  1. A5
  2. B46
  3. C11
  4. D95
Show answer & solution

Answer: B. 46

Solution

Rule: ×2 + 1 (2, 5, 11, 23, 47, 95). 23 × 2 + 1 = 47, not 46. Answer: 46

Q43.

Find the wrong number in the series: 1, 8, 27, 64, 124, 216

  1. A8
  2. B27
  3. C124
  4. D216
Show answer & solution

Answer: C. 124

Solution

Perfect cubes 1, 8, 27, 64, 125, 216. The fifth term should be 5³ = 125, not 124. Answer: 124

Q44.

Find the wrong number in the series: 7, 8, 18, 57, 232, 1145

  1. A8
  2. B18
  3. C232
  4. D1145
Show answer & solution

Answer: D. 1145

Solution

Rule: ×1+1, ×2+2, ×3+3, ×4+4, ×5+5: 7, 8, 18, 57, 232, 1165. 232 × 5 + 5 = 1165, not 1145. Answer: 1145

Q45.

Find the next number in the series: 1, 4, 10, 22, 46, 94, ?

  1. A190
  2. B188
  3. C192
  4. D186
Show answer & solution

Answer: A. 190

Solution

Rule: previous × 2 + 2 (1×2+2 = 4, 4×2+2 = 10, 10×2+2 = 22, 22×2+2 = 46, 46×2+2 = 94). Next: 94 × 2 + 2 = 190 Answer: 190

Ready to test yourself? 10 fresh Number Series questions, timed, with solutions at the end.

Start the quiz

Related topics

Letter & Alphabet SeriesCoding-DecodingBlood RelationsDirection SenseSeating ArrangementPuzzlesSyllogismsStatements, Assumptions & ConclusionsAnalogies & Odd One OutClocks & CalendarsRanking & OrderInequalitiesData SufficiencyToday's Daily Quiz · 5 questions

Practise this with Sam

A real mock interview, out loud, with an honest scorecard. Free to start.

Start free