Number & Letter Sequences
50 Class 6 IMO Mathematics Olympiad practice questions on number & letter sequences, part of the Patterns & Sequences topic area. Every question below includes the correct answer and a full explanation.
Practice this topic interactively →1. Find the next number: 5, 10, 15, 20, ?
- A.22
- B.24
- C.25
- D.30
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Answer: C. 25
Each term increases by 5.
2. Find the next term: 3, 6, 12, 24, ?
- A.36
- B.42
- C.48
- D.54
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Answer: C. 48
Each term doubles the previous one: 24 × 2 = 48.
3. Find the next number: 7, 14, 21, 28, ?
- A.32
- B.35
- C.36
- D.42
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Answer: B. 35
Each term increases by 7.
4. Find the next number: 2, 10, 18, 26, 34, ?
- A.50
- B.34
- C.58
- D.42
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Answer: D. 42
Each term increases by 8, so the next term is 34 + 8 = 42.
5. Find the next number: 9, 17, 25, 33, 41, ?
- A.65
- B.49
- C.57
- D.41
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Answer: B. 49
Each term increases by 8, so the next term is 41 + 8 = 49.
6. Find the next number: 4, 6, 8, 10, 12, ?
- A.16
- B.18
- C.14
- D.12
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Answer: C. 14
Each term increases by 2, so the next term is 12 + 2 = 14.
7. Find the next number: 1, 4, 9, 16, ?
- A.20
- B.23
- C.25
- D.36
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Answer: C. 25
These are perfect squares: 1², 2², 3², 4², next is 5² = 25.
8. Find the missing letter: A, C, E, G, ?
- A.H
- B.I
- C.J
- D.K
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Answer: B. I
Positions 1, 3, 5, 7 — skipping one letter each time. Next is position 9, which is I.
9. Find the next number: 81, 27, 9, 3, ?
- A.0
- B.1
- C.2
- D.−3
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Answer: B. 1
Each term is divided by 3: 3 ÷ 3 = 1.
10. Find the missing letter: Z, X, V, T, ?
- A.Q
- B.R
- C.S
- D.U
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Answer: B. R
Positions: 26, 24, 22, 20 — decreasing by 2 each time. Next is 18, which is R.
11. Find the missing number: 4, 9, 16, 25, ?, 49
- A.30
- B.32
- C.36
- D.40
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Answer: C. 36
These are squares of 2, 3, 4, 5, 6, 7 — the missing one is 6² = 36.
12. A pattern follows: 3, 8, 15, 24, 35, ?. What is the next number?
- A.44
- B.46
- C.48
- D.50
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Answer: C. 48
Differences are 5, 7, 9, 11 — increasing by 2 each time. Next difference is 13: 35+13=48.
13. If A=1, B=2, C=3, ... Z=26, what is the value of the word MATH?
- A.38
- B.40
- C.42
- D.44
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Answer: C. 42
M=13, A=1, T=20, H=8. 13+1+20+8=42.
14. Find the next number: 2, 8, 14, 20, 26, ?
- A.26
- B.44
- C.32
- D.38
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Answer: C. 32
Each term increases by 6, so the next term is 26 + 6 = 32.
15. Find the next number: 1, 7, 13, 19, 25, ?
- A.43
- B.25
- C.31
- D.37
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Answer: C. 31
Each term increases by 6, so the next term is 25 + 6 = 31.
16. Find the next number: 2, 5, 8, 11, 14, ?
- A.17
- B.23
- C.14
- D.20
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Answer: A. 17
Each term increases by 3, so the next term is 14 + 3 = 17.
17. Find the next number: 9, 13, 17, 21, 25, ?
- A.33
- B.37
- C.29
- D.25
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Answer: C. 29
Each term increases by 4, so the next term is 25 + 4 = 29.
18. Find the next number: 6, 14, 22, 30, 38, ?
- A.62
- B.54
- C.46
- D.38
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Answer: C. 46
Each term increases by 8, so the next term is 38 + 8 = 46.
19. Find the next number: 7, 15, 23, 31, 39, ?
- A.55
- B.63
- C.47
- D.39
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Answer: C. 47
Each term increases by 8, so the next term is 39 + 8 = 47.
20. Find the next number: 2, 6, 10, 14, 18, ?
- A.26
- B.30
- C.18
- D.22
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Answer: D. 22
Each term increases by 4, so the next term is 18 + 4 = 22.
21. Find the next number: 7, 13, 19, 25, 31, ?
- A.37
- B.43
- C.49
- D.31
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Answer: A. 37
Each term increases by 6, so the next term is 31 + 6 = 37.
22. Find the next number: 9, 12, 15, 18, 21, ?
- A.30
- B.24
- C.27
- D.21
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Answer: B. 24
Each term increases by 3, so the next term is 21 + 3 = 24.
23. Find the next number: 6, 10, 14, 18, 22, ?
- A.34
- B.26
- C.30
- D.22
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Answer: B. 26
Each term increases by 4, so the next term is 22 + 4 = 26.
24. Find the next number: 5, 12, 19, 26, 33, ?
- A.54
- B.40
- C.47
- D.33
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Answer: B. 40
Each term increases by 7, so the next term is 33 + 7 = 40.
25. If 4 → 16 and 7 → 49, then 7 → ?
- A.14
- B.21
- C.50
- D.49
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Answer: D. 49
Each number maps to its own square (4→16, 7→49), so 7 → 7² = 49.
26. If 4 → 16 and 7 → 49, then 8 → ?
- A.64
- B.65
- C.16
- D.24
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Answer: A. 64
Each number maps to its own square (4→16, 7→49), so 8 → 8² = 64.
27. Find the next number: 100, 90, 81, 73, ?
- A.64
- B.65
- C.66
- D.67
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Answer: C. 66
The differences are −10, −9, −8 — decreasing by 1 each time. Next difference is −7, so 73 − 7 = 66.
28. Find the next number: 2, 3, 5, 8, 13, ?
- A.18
- B.20
- C.21
- D.24
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Answer: C. 21
Each term is the sum of the two before it: 8+13 = 21.
29. Find the next number: 2, 5, 11, 23, 47, ?
- A.93
- B.94
- C.95
- D.96
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Answer: C. 95
Each term follows the rule ×2+1: 47×2+1 = 95.
30. Find the next term: 1, 8, 27, 64, ?
- A.100
- B.120
- C.125
- D.144
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Answer: C. 125
These are cubes: 1³, 2³, 3³, 4³, next is 5³ = 125.
31. Which number replaces the question mark? 2, 5, 11, 23, 47, ?
- A.93
- B.94
- C.95
- D.96
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Answer: C. 95
Each term follows ×2+1: 47×2+1=95.
32. Find the missing term: AZ, BY, CX, DW, ?
- A.EV
- B.EU
- C.FV
- D.EW
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Answer: A. EV
First letters go A,B,C,D,E (forward); second letters go Z,Y,X,W,V (backward). Next is EV.
33. A number machine changes 4 to 13, 7 to 22, and 10 to 31. Which rule is used?
- A.×2 + 5
- B.×3 + 1
- C.×3 − 1
- D.×4 − 3
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Answer: B. ×3 + 1
4×3+1=13, 7×3+1=22, 10×3+1=31 — all match ×3+1.
34. Which pair has the same relationship as 8 : 64?
- A.5 : 20
- B.6 : 36
- C.7 : 42
- D.9 : 63
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Answer: B. 6 : 36
8 : 64 is n : n² (8² = 64). Only 6 : 36 fits this same rule (6² = 36).
35. Find the next number: 6, 11, 16, 21, 26, ?
- A.26
- B.36
- C.41
- D.31
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Answer: D. 31
Each term increases by 5, so the next term is 26 + 5 = 31.
36. Find the next number: 7, 10, 13, 16, 19, ?
- A.19
- B.25
- C.28
- D.22
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Answer: D. 22
Each term increases by 3, so the next term is 19 + 3 = 22.
37. Find the next number: 5, 10, 15, 20, 25, ?
- A.40
- B.25
- C.30
- D.35
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Answer: C. 30
Each term increases by 5, so the next term is 25 + 5 = 30.
38. Find the next number: 4, 11, 18, 25, 32, ?
- A.53
- B.32
- C.39
- D.46
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Answer: C. 39
Each term increases by 7, so the next term is 32 + 7 = 39.
39. Find the next number: 8, 11, 16, 23, ?
- A.30
- B.36
- C.34
- D.32
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Answer: D. 32
The differences are 3, 5, 7 — increasing by 2 each time. The next difference is 9, so 23 + 9 = 32.
40. Find the missing term: B, D, H, N, ?
- A.T
- B.U
- C.V
- D.W
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Answer: C. V
Positions: B=2, D=4, H=8, N=14 — differences are 2, 4, 6 (increasing by 2). Next difference is 8, so 14+8=22, which is V.
41. Find the next number: 1, 2, 4, 7, 11, 16, ?
- A.20
- B.21
- C.22
- D.23
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Answer: C. 22
The differences are 1, 2, 3, 4, 5 — increasing by 1 each time. Next difference is 6, so 16+6=22.
42. Find the next letter group: AB, DE, GH, JK, ?
- A.LM
- B.MN
- C.NO
- D.MO
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Answer: B. MN
The first letter of each group moves 3 positions ahead each time: A, D, G, J, next is M — followed by N.
43. Find the next number: 2, 4, 6, 8, 10, ?
- A.16
- B.10
- C.14
- D.12
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Answer: D. 12
Each term increases by 2, so the next term is 10 + 2 = 12.
44. Find the next number: 3, 7, 11, 15, 19, ?
- A.27
- B.19
- C.31
- D.23
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Answer: D. 23
Each term increases by 4, so the next term is 19 + 4 = 23.
45. Find the next number: 7, 12, 17, 22, 27, ?
- A.37
- B.27
- C.32
- D.42
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Answer: C. 32
Each term increases by 5, so the next term is 27 + 5 = 32.
46. Complete: AZ, BY, CX, DW, ?
- A.FV
- B.EU
- C.EW
- D.EV
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Answer: D. EV
First letters go A,B,C,D,E (forward); second letters go Z,Y,X,W,V (backward). Next is EV.
47. Find the next number: 9, 12, 17, 24, ?
- A.31
- B.35
- C.37
- D.33
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Answer: D. 33
The differences are 3, 5, 7 — increasing by 2 each time. The next difference is 9, so 24 + 9 = 33.
48. Find the next number: 3, 6, 11, 18, ?
- A.25
- B.29
- C.31
- D.27
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Answer: D. 27
The differences are 3, 5, 7 — increasing by 2 each time. The next difference is 9, so 18 + 9 = 27.
49. Find the next number: 6, 11, 21, 36, 56, ?
- A.76
- B.79
- C.81
- D.84
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Answer: C. 81
The differences are 5, 10, 15, 20 — increasing by 5 each time. Next difference is 25, so 56+25=81.
50. If 4 → 16 and 7 → 49, then 9 → ?
- A.81
- B.27
- C.82
- D.18
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Answer: A. 81
Each number maps to its own square (4→16, 7→49), so 9 → 9² = 81.