Read the sequence as a process

A series is a repeated operation, sometimes two or more interleaved operations. Start with adjacent differences. If they are constant, the series is arithmetic; if successive terms have a constant ratio, it may be geometric. If differences change, inspect their differences. Squares, cubes and triangular numbers are common, but a sequence should not be labelled from a single term. Alternating odd and even positions often form two simpler series. Write terms in two rows if the one-row pattern is unclear.

A practical decision order

For 6, 11, 18, 27, ?, the differences are 5, 7, 9; the next difference is 11, giving 38. For 4, 8, 5, 10, 6, 12, ?, the odd positions are 4, 5, 6, so the next odd-position term is 7. The even positions double each preceding odd term. If digits are mixed with letters, solve each component separately. For a term such as E6, F8, G10, the letter advances one and the number advances two. A correct option must satisfy both components.

Guard against overfitting

With only a few terms, many artificial formulas can fit. Competitive-exam series generally favour a short repeatable rule. Test the proposed rule at every transition, including the last visible one. When numbers grow quickly, compare multiplication plus or minus a small constant. If they alternate between large and small values, check whether two sequences were interleaved. For a missing middle term, test from both sides; a rule that only predicts the next term may fail the earlier segment.

Speed and review

Spend a short first pass on differences, ratios, odd/even positions and familiar square or cube patterns. If none fits, park the item and return after easier questions. Do not spend the whole section inventing high-degree polynomials. Keep a scratch column for differences; it is faster and safer than holding six changes in memory. In review, record the exact pattern family and the step where your predicted series first diverged.

Practice — 50 questions

Attempt every item before reading the answers below. Figure questions require the printed or on-screen diagram.

1. What is the 10th term of the following series?
7, 12, 6, 11, 5, 10, …

A. 30 B. 3 C. 8 D. 2

2. Find the missing term in the series: 3, 9, 27, 81, 243, ?

A. 547 B. 729 C. 405 D. 637

3. Find the missing term in the series: 5, 10, 20, ?, 80, 160

A. 41 B. 40 C. 30 D. 39

4. Find the wrong term in the series: 29, 36, 43, 46, 57, 64

A. 57 B. 64 C. 46 D. 43

5. What is the 8th term of the following series?
2, 9, 18, 29, 42, 57, …

A. 114 B. 87 C. 74 D. 93

6. Find the wrong term in the series: 51, 57, 63, 69, 75, 83

A. 51 B. 83 C. 63 D. 75

7. Find the missing term in the series: 14, 19, ?, 29, 34, 39

A. 18 B. 25 C. 30 D. 24

8. Find the missing term in the series: 11, 19, 14, 22, 17, ?

A. 12 B. 29 C. 28 D. 25

9. Find the wrong term in the series: 9, 45, 225, 4641, 5625, 28125

A. 9 B. 4641 C. 225 D. 28125

10. Find the missing term in the series: 11, 20, 4, ?, -3, 6

A. 11 B. 15 C. 13 D. -12

11. Find the missing term in the series: 726, 997, ?, 1725, 2194, 2741

A. 1268 B. 1256 C. 1076 D. 1328

12. Find the missing term in the series: 6, 24, 96, 384, 1536, ?

A. 6911 B. 6144 C. 6145 D. 2688

13. Find the missing term in the series: 8, 10, 17, 29, 46, ?

A. 63 B. 59 C. 76 D. 68

14. Which number will replace the question mark (?) in the given series?
34, 3, 42, 9, 50, 27, 58, 81, ?, 243

A. 67 B. 66 C. 220 D. 104

15. Find the wrong term in the series: 18, 37, 17, 34, 12, 31

A. 17 B. 12 C. 31 D. 18

16. Find the missing term in the series: 7, 11, 13, 17, 19, ?

A. 26 B. 23 C. 22 D. 21

17. Find the missing term in the series: 9, 13, 21, 33, ?, 69

A. 49 B. 57 C. 45 D. 41

18. Which number will replace the question mark (?) in the given series?
5, 56, 7, 49, 11, 42, 13, ?

A. 44 B. 31 C. 29 D. 35

19. Find the missing term in the series: 64, 192, 96, ?, 144, 432

A. 288 B. 242 C. 289 D. 380

20. Find the missing term in the series: 8, 13, 1, ?, -6, -1

A. 5 B. -11 C. 6 D. 9

21. Which number comes immediately after -5 in the following series?
19, 28, 11, 20, 3, 12, -5, …

A. 4 B. -13 C. 5 D. -22

22. Find the missing term in the series: 130, 221, 348, 517, ?, 1005

A. 686 B. 733 C. 734 D. 624

23. Find the missing term in the series: 144, 720, 360, 1800, ?, 4500

A. 3240 B. 900 C. 354 D. 899

24. Find the missing term in the series: 4, 20, ?, 376, 1526, 6132

A. 36 B. 857 C. 90 D. 1622

25. Find the wrong term in the series: 6, 15, 26, 46, 77, 120

A. 120 B. 77 C. 26 D. 46

26. Find the missing term in the series: E3, F5, G7, H9, ?

A. J12 B. I13 C. I11 D. I9

27. Find the missing term in the series: V3, W4, X5, Y6, ?

A. Z7 B. Z6 C. Y7 D. X7

28. Find the missing term in the series: C9, E11, G13, I15, ?

A. J16 B. L18 C. K17 D. K18

29. Find the missing term in the series: E1, F4, G7, H10, ?

A. I13 B. H12 C. I11 D. I14

30. Find the missing term in the series: I3, K8, M13, O18, ?

A. Q25 B. R23 C. Q21 D. Q23

31. Find the missing term in the series: D6, E7, F8, G9, ?

A. H11 B. H10 C. I10 D. H9

32. Find the missing term in the series: E1, G4, I7, K10, ?

A. M13 B. M12 C. M11 D. K13

33. Find the missing term in the series: O4, Q7, S10, U13, ?

A. W16 B. W17 C. X17 D. W15

34. Find the missing term in the series: N1, O4, P9, Q16, ?

A. R25 B. R27 C. Q24 D. S26

35. Find the missing term in the series: B1, C4, D7, E10, ?

A. F13 B. F15 C. G13 D. F12

36. Find the missing term in the series: N7, O8, P9, Q10, ?

A. S12 B. R12 C. Q10 D. R11

37. Find the missing term in the series: A2, C4, E6, G8, ?

A. I10 B. J10 C. J11 D. H10

38. Find the missing term in the series: Q1, S4, U9, W16, ?

A. X24 B. Z26 C. Y25 D. W25

39. Find the missing term in the series: L5, N6, P7, R8, ?

A. T7 B. T10 C. S8 D. T9

40. Find the missing term in the series: I8, K12, M16, O20, ?

A. O24 B. P23 C. Q24 D. R25

41. Find the missing term in the series: G3, I6, K12, M24, ?

A. O46 B. P49 C. O48 D. N48

42. Find the missing term in the series: R1, S6, T11, U16, ?

A. V21 B. W21 C. V20 D. V23

43. Find the missing term in the series: E8, F10, G12, H14, ?

A. I18 B. J17 C. H16 D. I16

44. Find the missing term in the series: L7, N11, P15, R19, ?

A. T23 B. T22 C. V23 D. S23

45. Find the missing term in the series: C1, D4, E9, F16, ?

A. G25 B. E25 C. G23 D. F24

46. Find the missing term in the series: I1, K4, M9, O16, ?

A. P24 B. Q25 C. R25 D. S25

47. Find the missing term in the series: 5, 7, 9, 18, 36, ?

A. 72 B. 86 C. 65 D. 73

48. 3, -4, -11 is to -18 as 18, 11, 4 is to ?

A. -3 B. -5 C. 0 D. -1

49. Find the missing term in the series: 7, 13, 19, 38, 76, ?

A. 152 B. 153 C. 168 D. 182

50. Find the missing term in the series: 11, 15, 19, 57, 171, ?

A. 564 B. 411 C. 513 D. 512

Answers and explanations

After checking the key, explain the rule or diagram transformation to yourself before moving on.

1. C. Pattern: alternately +5 and -6. Continuing from the 6th term 10: 4, 9, 3, 8. So the 10th term is 8.

APRS26-03-01 | Nth term | Easy

2. B. Pattern: multiply by 3 each time. The complete series is 3, 9, 27, 81, 243, 729, so the missing term is 729.

APRS26-03-02 | Missing term | Easy

3. B. Pattern: multiply by 2 each time. The complete series is 5, 10, 20, 40, 80, 160, so the missing term is 40.

APRS26-03-03 | Missing term | Easy

4. C. Pattern: add +7 each time. The correct series is 29, 36, 43, 50, 57, 64; "46" (shown in place of 50) breaks the pattern.

APRS26-03-04 | Wrong term | Easy

5. D. Pattern: the differences are 7, 9, 11, … (difference increases by 2 each time). Continuing from the 6th term 57: 74, 93. So the 8th term is 93.

APRS26-03-05 | Nth term | Easy

6. B. Pattern: add +6 each time. The correct series is 51, 57, 63, 69, 75, 81; "83" (shown in place of 81) breaks the pattern.

APRS26-03-06 | Wrong term | Easy

7. D. Pattern: add +5 each time. The complete series is 14, 19, 24, 29, 34, 39, so the missing term is 24.

APRS26-03-07 | Missing term | Easy

8. D. Pattern: alternately +8 and -5. The complete series is 11, 19, 14, 22, 17, 25, so the missing term is 25.

APRS26-03-08 | Missing term | Easy

9. B. Pattern: multiply by 5 each time. The correct series is 9, 45, 225, 1125, 5625, 28125; "4641" (shown in place of 1125) breaks the pattern.

APRS26-03-09 | Wrong term | Medium

10. C. Pattern: alternately +9 and -16. The complete series is 11, 20, 4, 13, -3, 6, so the missing term is 13.

APRS26-03-10 | Missing term | Medium

11. D. Pattern: n^3 − 3 for n = 9, 10, 11, …. The complete series is 726, 997, 1328, 1725, 2194, 2741, so the missing term is 1328.

APRS26-03-11 | Missing term | Medium

12. B. Pattern: multiply by 4 each time. The complete series is 6, 24, 96, 384, 1536, 6144, so the missing term is 6144.

APRS26-03-12 | Missing term | Medium

13. D. Pattern: the differences are 2, 7, 12, … (difference increases by 5 each time). The complete series is 8, 10, 17, 29, 46, 68, so the missing term is 68.

APRS26-03-13 | Missing term | Medium

14. B. The series is made of two alternating sub-series. Odd-position terms: 34, 42, 50, 58, 66 (add +8 each time). Even-position terms: 3, 9, 27, 81, 243 (multiply by 3 each time). The blank is the 5th term of the odd-position series, so it is 66.

APRS26-03-14 | Interleaved series | Medium

15. A. Pattern: alternately +19 and -22. The correct series is 18, 37, 15, 34, 12, 31; "17" (shown in place of 15) breaks the pattern.

APRS26-03-15 | Wrong term | Medium

16. B. Pattern: consecutive prime numbers. The complete series is 7, 11, 13, 17, 19, 23, so the missing term is 23.

APRS26-03-16 | Missing term | Medium

17. A. Pattern: the differences are 4, 8, 12, … (difference increases by 4 each time). The complete series is 9, 13, 21, 33, 49, 69, so the missing term is 49.

APRS26-03-17 | Missing term | Medium

18. D. The series is made of two alternating sub-series. Odd-position terms: 5, 7, 11, 13 (consecutive prime numbers). Even-position terms: 56, 49, 42, 35 (add -7 each time). The blank is the 4th term of the even-position series, so it is 35.

APRS26-03-18 | Interleaved series | Medium

19. A. Pattern: alternately ×3 and ÷2. The complete series is 64, 192, 96, 288, 144, 432, so the missing term is 288.

APRS26-03-19 | Missing term | Medium

20. C. Pattern: alternately +5 and -12. The complete series is 8, 13, 1, 6, -6, -1, so the missing term is 6.

APRS26-03-20 | Missing term | Medium

21. A. Pattern: alternately +9 and -17. Continuing from the 7th term -5: 4. So the 8th term is 4.

APRS26-03-21 | Nth term | Medium

22. C. Pattern: n^3 + 5 for n = 5, 6, 7, …. The complete series is 130, 221, 348, 517, 734, 1005, so the missing term is 734.

APRS26-03-22 | Missing term | Difficult

23. B. Pattern: alternately ×5 and ÷2. The complete series is 144, 720, 360, 1800, 900, 4500, so the missing term is 900.

APRS26-03-23 | Missing term | Difficult

24. C. Pattern: each term = previous term × 4 + (4, 10, 16, … — the addend grows by 6). The complete series is 4, 20, 90, 376, 1526, 6132, so the missing term is 90.

APRS26-03-24 | Missing term | Difficult

25. A. Pattern: each term = sum of the previous two terms + 5. The correct series is 6, 15, 26, 46, 77, 128; "120" (shown in place of 128) breaks the pattern.

APRS26-03-25 | Wrong term | Difficult

26. C. Pattern: the letter advances by 1 and the number advances by 2 at each step. The complete series is E3, F5, G7, H9, I11, so the missing term is I11.

APRS26-03-26 | Joint letter-number series | Easy

27. A. Pattern: the letter advances by 1 and the number advances by 1 at each step. The complete series is V3, W4, X5, Y6, Z7, so the missing term is Z7.

APRS26-03-27 | Joint letter-number series | Easy

28. C. Pattern: the letter advances by 2 and the number advances by 2 at each step. The complete series is C9, E11, G13, I15, K17, so the missing term is K17.

APRS26-03-28 | Joint letter-number series | Easy

29. A. Pattern: the letter advances by 1 and the number advances by 3 at each step. The complete series is E1, F4, G7, H10, I13, so the missing term is I13.

APRS26-03-29 | Joint letter-number series | Easy

30. D. Pattern: the letter advances by 2 and the number advances by 5 at each step. The complete series is I3, K8, M13, O18, Q23, so the missing term is Q23.

APRS26-03-30 | Joint letter-number series | Easy

31. B. Pattern: the letter advances by 1 and the number advances by 1 at each step. The complete series is D6, E7, F8, G9, H10, so the missing term is H10.

APRS26-03-31 | Joint letter-number series | Easy

32. A. Pattern: the letter advances by 2 and the number advances by 3 at each step. The complete series is E1, G4, I7, K10, M13, so the missing term is M13.

APRS26-03-32 | Joint letter-number series | Easy

33. A. Pattern: the letter advances by 2 and the number advances by 3 at each step. The complete series is O4, Q7, S10, U13, W16, so the missing term is W16.

APRS26-03-33 | Joint letter-number series | Easy

34. A. Pattern: the letter advances by 1 and the number is the square of its position (1², 2², 3², ...). The complete series is N1, O4, P9, Q16, R25, so the missing term is R25.

APRS26-03-34 | Joint letter-number series | Medium

35. A. Pattern: the letter advances by 1 and the number advances by 3 at each step. The complete series is B1, C4, D7, E10, F13, so the missing term is F13.

APRS26-03-35 | Joint letter-number series | Medium

36. D. Pattern: the letter advances by 1 and the number advances by 1 at each step. The complete series is N7, O8, P9, Q10, R11, so the missing term is R11.

APRS26-03-36 | Joint letter-number series | Medium

37. A. Pattern: the letter advances by 2 and the number advances by 2 at each step. The complete series is A2, C4, E6, G8, I10, so the missing term is I10.

APRS26-03-37 | Joint letter-number series | Medium

38. C. Pattern: the letter advances by 2 and the number is the square of its position (1², 2², 3², ...). The complete series is Q1, S4, U9, W16, Y25, so the missing term is Y25.

APRS26-03-38 | Joint letter-number series | Medium

39. D. Pattern: the letter advances by 2 and the number advances by 1 at each step. The complete series is L5, N6, P7, R8, T9, so the missing term is T9.

APRS26-03-39 | Joint letter-number series | Medium

40. C. Pattern: the letter advances by 2 and the number advances by 4 at each step. The complete series is I8, K12, M16, O20, Q24, so the missing term is Q24.

APRS26-03-40 | Joint letter-number series | Medium

41. C. Pattern: the letter advances by 2 and the number is multiplied by 2 at each step (starting at 3). The complete series is G3, I6, K12, M24, O48, so the missing term is O48.

APRS26-03-41 | Joint letter-number series | Medium

42. A. Pattern: the letter advances by 1 and the number advances by 5 at each step. The complete series is R1, S6, T11, U16, V21, so the missing term is V21.

APRS26-03-42 | Joint letter-number series | Medium

43. D. Pattern: the letter advances by 1 and the number advances by 2 at each step. The complete series is E8, F10, G12, H14, I16, so the missing term is I16.

APRS26-03-43 | Joint letter-number series | Medium

44. A. Pattern: the letter advances by 2 and the number advances by 4 at each step. The complete series is L7, N11, P15, R19, T23, so the missing term is T23.

APRS26-03-44 | Joint letter-number series | Medium

45. A. Pattern: the letter advances by 1 and the number is the square of its position (1², 2², 3², ...). The complete series is C1, D4, E9, F16, G25, so the missing term is G25.

APRS26-03-45 | Joint letter-number series | Medium

46. B. Pattern: the letter advances by 2 and the number is the square of its position (1², 2², 3², ...). The complete series is I1, K4, M9, O16, Q25, so the missing term is Q25.

APRS26-03-46 | Joint letter-number series | Medium

47. A. Pattern: the first three terms form an AP with common difference 2 (5, 7, 9), then the series switches to a GP with common ratio 2 starting from 9 × 2 (18, 36, 72). So the complete series is 5, 7, 9, 18, 36, 72, and the missing term is 72.

APRS26-03-47 | Mixed sub-pattern series | Difficult

48. A. From the first set, the rule is: each term = previous term - 7 (so 3, -4, -11, -18). Applying the same rule to 18, 11, 4 gives -3.

APRS26-03-48 | Series analogy | Difficult

49. A. Pattern: the first three terms form an AP with common difference 6 (7, 13, 19), then the series switches to a GP with common ratio 2 starting from 19 × 2 (38, 76, 152). So the complete series is 7, 13, 19, 38, 76, 152, and the missing term is 152.

APRS26-03-49 | Mixed sub-pattern series | Difficult

50. C. Pattern: the first three terms form an AP with common difference 4 (11, 15, 19), then the series switches to a GP with common ratio 3 starting from 19 × 3 (57, 171, 513). So the complete series is 11, 15, 19, 57, 171, 513, and the missing term is 513.

APRS26-03-50 | Mixed sub-pattern series | Difficult