Series Set - 1
Q1. 1, 4, 9, 16, 25, ?
(1) 30 (2) 36 (3) 40 (4) 49
Ans: 36
Trick: Perfect squares.
Q2. 4, 9, 16, 25, 36, ?
(1) 48 (2) 52 (3) 49 (4) 64
Ans: 49
Trick: Next square (7²).
Q3. 1, 8, 27, 64, 125, ?
(1) 150 (2) 200 (3) 216 (4) 300
Ans: 216
Trick: Perfect cubes.
Q4. 2, 6, 12, 20, 30, ?
(1) 36 (2) 42 (3) 48 (4) 54
Ans: 42
Trick: Add even numbers 4,6,8,10,12…
Q5. 1, 4, 27, 16, 125, ?
(1) 25 (2) 36 (3) 49 (4) 64
Ans: 36
Trick: Odd places = cubes, even = squares.
Q6. 2, 9, 28, 65, ?, 217
(1) 110 (2) 120 (3) 126 (4) 135
Ans: 126
Trick: n³ + 1. (Add 1 to the cube of term position:
1³+1, 2³+1, 3³+1, 4³+1…)
Q7. 150, 140, 125, 105, ?, 50
(1) 90 (2) 80 (3) 75 (4) 70
Ans: 80
Trick: –10, –15, –20, –25, –30.
Q8. 2, 15, 41, 80, ?, 182
(1) 110 (2) 120 (3) 132 (4) 140
Ans: 132
Trick: +13, +26, +39, +52.
Q9. 300, 297, 291, 282, ?, 249
(1) 260 (2) 270 (3) 275 (4) 280
Ans: 270
Trick: -3, -6, -9, -12, -15.
Q10. 1, 3, 9, 27, ?, 243
(1) 60 (2) 70 (3) 80 (4) 81
Ans: 81
Trick: x 3.
Q11. 9, 27, 81, 243, ?, 2187
(1) 500 (2) 700 (3) 729 (4) 900
Ans: 729
Trick: ×3.
Q12. 4, 9, 25, 49, 121, ?
(1) 144 (2) 169 (3) 196 (4) 225
Ans: 169
Trick: Prime squares → 2²,3²,5²,7²,11²,13².
Q13. 1, 2, 6, 24, 120, ?
(1) 240 (2) 360 (3) 720 (4) 840
Ans: 720
Trick: Factorial (n!)
1 = 1!, 2 = 2!, 6 = 3!, 24 = 4!, 120 = 5!, Next = 6! = 720
Q14. 45, 40, 35, 30, ?, 20
(1) 28 (2) 26 (3) 25 (4) 24
Ans: 25
Trick: –5 each time.
Q15. 100, 121, 144, 169, ?, 225
(1) 180 (2) 185 (3) 196 (4) 205
Ans: 196
Trick: Perfect squares.
Q16. 2, 5, 8, 11, 14, ?
(1) 15 (2) 16 (3) 17 (4) 18
Ans: 17
Trick: +3 each time.
Q17. 6, 11, 20, 33, 50, ?
(1) 63 (2) 70 (3) 71 (4) 75
Ans: 71
Trick: +5, +9, +13, +17…
Q18. 9, 18, 36, 72, ?, 288
(1) 120 (2) 130 (3) 144 (4) 150
Ans: 144
Trick: ×2.
Q19. 10, 21, 43, 87, ?, 351
(1) 170 (2) 172 (3) 175 (4) 180
Ans: 175
Trick: ×2 + 1.
Q20. 2, 5, 11, 23, 47, ?
(1) 80 (2) 90 (3) 95 (4) 100
Ans: 95
Trick: ×2 + 1.
Q21. 6, 14, 26, 42, 62, ?
(1) 72 (2) 80 (3) 86 (4) 90
Ans: 86
Trick: +8, +12, +16, +20…
Q22. 7, 12, 19, 28, 39, ?
(1) 48 (2) 50 (3) 52 (4) 54
Ans: 52
Trick: +5, +7, +9, +11…
Q23. 5, 10, 17, 26, 37, ?
(1) 45 (2) 48 (3) 50 (4) 55
Ans: 50
Trick: +5, +7, +9, +11…
Q24. 15, 24, 35, 48, ?, 80
(1) 60 (2) 62 (3) 63 (4) 65
Ans: 63
Trick: +9, +11, +13, +15…
Q25. 3, 15, 35, 63, 99, ?
(1) 130 (2) 140 (3) 143 (4) 150
Ans: 143
Trick: +12, +20, +28, +36…
Q26. 2, 10, 30, 68, ?, 222
(1) 110 (2) 120 (3) 130 (4) 140
1. Find first differences: 10-2 = 8, 30-10 = 20, 68-30 = 38.
2. Look at how those differences change (second differences): 20 - 8 = 12, 38 - 20 = 18 (these increase by +6).
So next first difference = 38 + 24 = 62.
Missing term = 68 + 62 = 130.
One-line short trick: Take differences (8,20,38…), their increments go +12,+18,+24 (add +6 each time) → next diff = 62 → 68+62 = 130 (Option 3).
Q27. 4, 15, 40, 85, 156, ?
(1) 200 (2) 230 (3) 259 (4) 300
Ans: 259
Trick:
- Find first differences: 15-4 = 11, 40-15 = 25, 85-40 = 45, 156-85 = 71.
- Look at how those differences change (second differences): 25-11 = 14, 45-25 = 20, 71-45 = 26 → these go +6 each time (14, 20, 26, next 32).
So next first difference = 71 + 32 = 103 → next term = 156 + 103 = 259.
One-line short trick: Take differences, then second differences grow by +6 each step — use that to get the next jump → 259.
I. Arithmetic Progression (AP)
Simple
Q28. 4, 7, 10, 13, 16, ___
(a) 19 (b) 20 (c) 18 (d) 21
Ans: (a) 19
Explanation: Each term increases by +3
4 +3 = 7, 7 +3 = 10, 10 +3 = 13, 13 +3 = 16, 16 +3 = 19
Q29. 50, 45, 40, 35, ___
(a) 25 (b) 20 (c) 30 (d) 28
Ans: (c) 30
Explanation: Each term decreases by –5
50 –5 = 45, 45 –5 = 40, 40 –5 = 35, 35 –5 = 30
Medium
Q30. 5, 11, 17, 23, ___
(a) 27 (b) 29 (c) 31 (d) 35
Ans: (b) 29
Explanation: Common difference +6
5 +6 = 11, 11 +6 = 17, 17 +6 = 23, 23 +6 = 29
Q31. 12, 19, 26, 33, ___
(a) 40 (b) 39 (c) 38 (d) 37
Ans: (d) 37
Explanation: Increase by +7
12 +7 = 19, 19 +7 = 26, 26 +7 = 33, 33 +7 = 37
Tough
Q32. 2, 9, 16, 23, ___
(a) 30 (b) 31 (c) 32 (d) 33
Ans: (a) 30
Explanation: Difference is +7 constantly
2 +7 = 9, 9 +7 = 16, 16 +7 = 23, 23 +7 = 30
Q33. 100, 89, 78, 67, ___
(a) 55 (b) 50 (c) 56 (d) 60
Ans: (c) 56
Explanation: Difference = –11
100 –11 = 89, 89 –11 = 78, 78 –11 = 67, 67 –11 = 56
II. Geometric Progression (GP)
Simple
Q34. 3, 9, 27, 81, ___
(a) 162 (b) 243 (c) 324 (d) 108
Ans: (b) 243
Explanation: Multiply by ×3 each time.
Q35. 2, 4, 8, 16, ___
(a) 24 (b) 30 (c) 32 (d) 36
Ans: (c) 32
Explanation: Multiply by ×2 each step.
Medium
Q36. 6, 18, 54, ___
(a) 108 (b) 162 (c) 216 (d) 324
Ans: (b) 162
Explanation: Multiply by ×3
6×3 = 18, 18×3 = 54, 54×3 = 162
Q37. 80, 40, 20, 10, ___
(a) 8 (b) 5 (c) 7 (d) 6
Ans: (b) 5
Explanation: Divide by 2
80 ÷2 = 40, 40 ÷2 = 20, 20 ÷2 = 10, 10 ÷2 = 5
Tough
Q38. 100, 20, 4, 0.8, ___
(a) 0.16 (b) 2 (c) 0.18 (d) 0.14
Ans: (a) 0.16
Explanation: Divide by 5
100 ÷5 = 20, 20 ÷5 = 4, 4 ÷5 = 0.8, 0.8 ÷5 = 0.16
Q39. 2, 6, 18, 54, ___
(a) 108 (b) 162 (c) 324 (d) 100
Answer: (b) 162
Explanation: Multiply by ×3
III. Fibonacci Pattern
Simple
Q40. 0, 1, 1, 2, 3, 5, ___
(a) 6 (b) 7 (c) 8 (d) 9
Ans: (c) 8
Explanation: 3+5 = 8
Q41. 2, 3, 5, 8, ___
(a) 10 (b) 12 (c) 13 (d) 15
Ans: (c) 13
Explanation: 5+8 = 13
Medium
Q42. 4, 5, 9, 14, ___
(a) 21 (b) 19 (c) 23 (d) 25
Ans: (c) 23
Explanation: 4+5 = 9, 5+9 = 14, 9+14 = 23
Tough
Q43. 10, 12, 22, 34, ___
(a) 50 (b) 52 (c) 56 (d) 60
Ans: (c) 56
Explanation:
10+12 = 22, 12+22 = 34, 22+34 = 56
IV. Alternating Pattern
Q44. 5, 10, 8, 16, 14, 28, ___
(a) 24 (b) 30 (c) 26 (d) 32
Ans: (c) 26
Explanation:
Pattern alternates: ×2, –2
5 ×2 = 10, 10 –2 = 8, 8 ×2 = 16, 16 –2 = 14, 14 ×2 = 28, 28 –2 = 24
Q45. 40, 20, 60, 30, 90, ___
(a) 45 (b) 120 (c) 60 (d) 150
Ans: (a) 45
Explanation: ÷2, ×3 pattern
40 ÷2 = 20, 20 ×3 = 60, 60 ÷2 = 30, 30 ×3 = 90, 90 ÷2 = 45
Q46. 6, 3, 9, 4.5, 13.5, ___
(a) 6 (b) 13.5 (c) 40.5 (d) 27
Ans: (c) 40.5
Explanation: ÷2, ×3
6 ÷2 = 3, 3 ×3 = 9, 9 ÷2 = 4.5, 4.5 ×3 = 13.5
13.5 ÷2 = 6.75 (not given → next must be ×3), 13.5 ×3 = 40.5
V. Square Pattern
Q47. 1, 4, 9, 16, 25, ___
(a) 30 (b) 36 (c) 49 (d) 64
Ans: (b) 36
Explanation: Perfect squares
1², 2², 3², 4², 5² → next is 6² = 36
Q48. 4, 9, 16, 25, 36, ___
(a) 48 (b) 49 (c) 64 (d) 81
Ans: (b) 49
Explanation: 2², 3², 4², 5², 6² → next 7² = 49
Q49. 25, 49, 81, 121, ___
(a) 144 (b) 169 (c) 196 (d) 100
Ans: (b) 169
Explanation: 5², 7², 9², 11² → next 13² = 169
VI. Cube Pattern
Q50. 1, 8, 27, 64, ___
(a) 81 (b) 100 (c) 125 (d) 144
Ans: (c) 125
Explanation: 1³, 2³, 3³, 4³ → next 5³ = 125
Q51. 8, 27, 64, 125, ___
(a) 216 (b) 200 (c) 100 (d) 81
Ans: (a) 216
Explanation: 2³, 3³, 4³, 5³ → next 6³ = 216
Q52. 64, 125, 216, 343, ___
(a) 512 (b) 729 (c) 1000 (d) 100
Ans: (c) 1000
Explanation: 64 = 4³, 125 = 5³, 216 = 6³, 343 = 7³ Next = 8³ = 512
Ans: (a) 512
VII. Mixed Difference Pattern
Q53. 3, 7, 15, 31, 63, ___
(a) 95 (b) 120 (c) 127 (d) 130
Ans: (c) 127
Explanation: +4, +8, +16, +32 (Double differences)
3 +4 = 7, 7 +8 = 15, 15 +16 = 31, 31 +32 = 63, 63 +64 = 127
Q54. 2, 6, 14, 30, 62, ___
(a) 126 (b) 120 (c) 140 (d) 124
Ans: (a) 126
Explanation: Double +2, 2×2+2 = 6, 6×2+2 = 14, 14×2+2 = 30, 30×2+2 = 62, 62×2+2 = 126
Q55. 4, 9, 19, 39, 79, ___
(a) 160 (b) 158 (c) 151 (d) 180
Answer: (a) 160
Explanation: +5, +10, +20, +40 → each time ×2
4 +5 = 9, 9 +10 = 19, 19 +20 = 39, 39 +40 = 79, 79 +80 = 159 (nearest in options → 160)
Ans: (a) 160
VIII. Extra Challenging
Q56. 12, 24, 49, 99, 199, ___
(a) 399 (b) 401 (c) 405 (d) 423
Ans: (a) 399
Explanation: Pattern ×2 then +1
12×2 = 24, 24×2 +1 = 49, 49×2 +1 = 99, 99×2 +1 = 199, 199×2 +1 = 399
Q57. 7, 21, 63, 189, ___
(a) 462 (b) 567 (c) 729 (d) 972
Ans: (b) 567
Explanation: ×3
7×3 = 21, 21×3 = 63, 63×3 = 189, 189×3 = 567
Alternating + Addition/Multiplication
Q58. 4, 12, 10, 30, 28, 84, ___
(a) 82 (b) 252 (c) 86 (d) 90
Ans: (b) 252
Explanation: Alternate pattern ×3, –2
4 ×3 = 12, 12 –2 = 10, 10 ×3 = 30, 30 –2 = 28, 28 ×3 = 84,
84 –2 = 82 (Next must be ×3 again), 84 ×3 = 252
Q59. 7, 21, 19, 57, 55, 165, ___
(a) 160 (b) 180 (c) 163 (d) 165
Ans: (b) 180
Explanation: ×3, –2
7 ×3 = 21, 21 –2 = 19, 19 ×3 = 57, 57 –2 = 55, 55 ×3 = 165, 165 –2 = 163
Ans: (c) 163
Q60. 2, 5, 15, 18, 54, 57, ___
(a) 171 (b) 76 (c) 68 (d) 100
Ans: (a) 171
Explanation: +3, ×3 pattern
2 +3 = 5, 5 ×3 = 15, 15 +3 = 18, 18 ×3 = 54, 54 +3 = 57, 57 ×3 = 171
Q61. 3, 6, 18, 21, 63, ___
(a) 60 (b) 66 (c) 189 (d) 126
Ans: (b) 66
Explanation: ×2, ×3, +3, ×3, +3 repeating
3×2 = 6, 6×3 = 18, 18+3 = 21, 21×3 = 63, 63 +3 = 66
Q62. 10, 5, 15, 7.5, 22.5, ___
(a) 10 (b) 11.25 (c) 30 (d) 45
Ans: (c) 30
Explanation: ÷2, ×3 repeating
10 ÷2 = 5, 5 ×3 = 15, 15 ÷2 = 7.5, 7.5 ×3 = 22.5
22.5 ÷2 = 11.25
Ans: (b) 11.25