Episode 8 — Aptitude and Reasoning / 8.24 — Series
8.24 Practice MCQs -- Series
Instructions: Find the next term, missing term, or wrong number as indicated. Answers and explanations are at the end.
Q1.
Find the next term: 5, 11, 17, 23, 29, ?
(a) 33
(b) 34
(c) 35
(d) 37
Q2.
Find the next term: 3, 9, 27, 81, ?
(a) 162
(b) 243
(c) 324
(d) 729
Q3.
Find the next term: 2, 6, 12, 20, 30, ?
(a) 40
(b) 42
(c) 44
(d) 36
Q4.
Find the next term: 1, 4, 9, 16, 25, ?
(a) 30
(b) 35
(c) 36
(d) 49
Q5.
Find the next term: 1, 1, 2, 3, 5, 8, 13, ?
(a) 18
(b) 20
(c) 21
(d) 26
Q6.
Find the next term: 2, 5, 11, 23, 47, ?
(a) 94
(b) 95
(c) 93
(d) 96
Q7.
Find the wrong number: 3, 7, 15, 31, 61, 127
(a) 7
(b) 15
(c) 61
(d) 127
Q8.
Find the next term: 1, 8, 27, 64, 125, ?
(a) 196
(b) 216
(c) 225
(d) 256
Q9.
Find the next term: 2, 3, 5, 7, 11, 13, ?
(a) 15
(b) 17
(c) 19
(d) 14
Q10.
Find the next term: 100, 96, 90, 82, 72, ?
(a) 62
(b) 60
(c) 58
(d) 56
Q11.
Find the next term: 1, 2, 6, 24, 120, ?
(a) 240
(b) 360
(c) 600
(d) 720
Q12.
Find the missing term: 2, 10, ?, 82, 162
(a) 28
(b) 32
(c) 34
(d) 40
Q13.
Find the next term: 4, 7, 12, 19, 28, ?
(a) 37
(b) 38
(c) 39
(d) 40
Q14.
Find the wrong number: 1, 4, 9, 16, 24, 36
(a) 4
(b) 16
(c) 24
(d) 36
Q15.
Find the next term: 3, 4, 8, 9, 27, 28, ?
(a) 29
(b) 56
(c) 81
(d) 82
Q16.
Find the next term: 7, 14, 28, 56, 112, ?
(a) 168
(b) 196
(c) 224
(d) 280
Q17.
Find the next term: 1, 3, 7, 15, 31, ?
(a) 47
(b) 55
(c) 63
(d) 62
Q18.
Find the next term: 5, 10, 20, 35, 55, ?
(a) 75
(b) 80
(c) 85
(d) 70
Q19.
Find the next term: 2, 6, 18, 54, 162, ?
(a) 324
(b) 486
(c) 648
(d) 972
Q20.
Find the wrong number: 2, 5, 10, 17, 26, 38, 50
(a) 10
(b) 26
(c) 38
(d) 50
Q21.
Find the next term: 0, 3, 8, 15, 24, 35, ?
(a) 46
(b) 48
(c) 50
(d) 44
Q22.
Find the next term: 11, 13, 17, 19, 23, 29, ?
(a) 31
(b) 33
(c) 35
(d) 37
Q23.
Find the next term: 4, 6, 12, 14, 28, 30, ?
(a) 32
(b) 60
(c) 62
(d) 56
Q24.
Find the next term: 1, 4, 27, 256, ?
(a) 625
(b) 1024
(c) 3125
(d) 5625
Q25.
Find the missing term: 1, 3, 6, 10, ?, 21, 28
(a) 14
(b) 15
(c) 16
(d) 13
Q26.
Find the next term: 2, 3, 5, 8, 13, 21, ?
(a) 29
(b) 31
(c) 34
(d) 42
Q27.
Find the next term: 1, 2, 5, 14, 41, ?
(a) 82
(b) 122
(c) 123
(d) 124
Q28.
Find the wrong number: 1, 2, 4, 8, 16, 34, 64
(a) 2
(b) 16
(c) 34
(d) 64
Q29.
Find the next term: 6, 13, 28, 59, ?
(a) 118
(b) 120
(c) 122
(d) 116
Q30.
Find the next term: 1, 5, 14, 30, 55, ?
(a) 81
(b) 85
(c) 91
(d) 100
Q31.
Find the next term: 2, 12, 36, 80, 150, ?
(a) 242
(b) 252
(c) 262
(d) 272
Q32.
Find the wrong number: 2, 3, 6, 18, 109, 1944
(a) 3
(b) 6
(c) 109
(d) 1944
Q33.
Find the next term: 4, 9, 25, 49, 121, ?
(a) 144
(b) 169
(c) 196
(d) 225
Q34.
Find the next term: 3, 5, 9, 15, 23, 33, ?
(a) 43
(b) 45
(c) 47
(d) 48
Q35.
Find the next term: 2, 2, 4, 12, 48, ?
(a) 96
(b) 192
(c) 240
(d) 288
Q36.
Find the missing term: 5, 11, 24, ?, 108, 221
(a) 48
(b) 49
(c) 50
(d) 51
Q37.
Find the next term: 10, 14, 22, 34, 50, ?
(a) 60
(b) 66
(c) 70
(d) 74
Q38.
Find the wrong number: 1, 1, 2, 3, 5, 8, 12, 21
(a) 2
(b) 8
(c) 12
(d) 21
Q39.
Find the next term: 3, 12, 48, 192, ?
(a) 384
(b) 576
(c) 768
(d) 960
Q40.
Find the next term: 7, 11, 19, 35, ?
(a) 51
(b) 57
(c) 63
(d) 67
Q41.
Find the next term: 1, 9, 25, 49, 81, ?
(a) 100
(b) 121
(c) 144
(d) 169
Q42.
Find the next term: 5, 6, 14, 15, 45, 46, ?
(a) 92
(b) 138
(c) 47
(d) 184
Q43.
Find the wrong number: 3, 5, 12, 38, 154, 768
(a) 5
(b) 12
(c) 38
(d) 768
Q44.
Find the next term: 2, 3, 5, 9, 17, 33, ?
(a) 49
(b) 55
(c) 63
(d) 65
Q45.
Find the next term: 0, 1, 1, 2, 4, 7, 13, ?
(a) 20
(b) 24
(c) 26
(d) 21
Answer Key
| Q | Ans | Q | Ans | Q | Ans | Q | Ans | Q | Ans |
|---|---|---|---|---|---|---|---|---|---|
| 1 | (c) | 10 | (b) | 19 | (b) | 28 | (c) | 37 | (c) |
| 2 | (b) | 11 | (d) | 20 | (c) | 29 | (c) | 38 | (c) |
| 3 | (b) | 12 | (c) | 21 | (b) | 30 | (c) | 39 | (c) |
| 4 | (c) | 13 | (c) | 22 | (a) | 31 | (b) | 40 | (d) |
| 5 | (c) | 14 | (c) | 23 | (b) | 32 | (c) | 41 | (b) |
| 6 | (b) | 15 | (c) | 24 | (c) | 33 | (b) | 42 | (b) |
| 7 | (c) | 16 | (c) | 25 | (b) | 34 | (b) | 43 | (d) |
| 8 | (b) | 17 | (c) | 26 | (c) | 35 | (c) | 44 | (d) |
| 9 | (b) | 18 | (b) | 27 | (b) | 36 | (b) | 45 | (b) |
Detailed Explanations
Q1. (c) 35
Arithmetic series with d=6. 29+6=35.
Q2. (b) 243
Geometric series with r=3. 81x3=243.
Q3. (b) 42
n(n+1): 1x2=2, 2x3=6, 3x4=12, 4x5=20, 5x6=30, 6x7=42.
Q4. (c) 36
Perfect squares: 1, 4, 9, 16, 25, 36 (6^2).
Q5. (c) 21
Fibonacci: 8+13=21.
Q6. (b) 95
Pattern: x2+1. 2x2+1=5, 5x2+1=11, 11x2+1=23, 23x2+1=47, 47x2+1=95.
Q7. (c) 61
Pattern: x2+1. 3,7,15,31,63,127. 31x2+1=63, not 61. Wrong: 61 (should be 63).
Q8. (b) 216
Perfect cubes: 6^3=216.
Q9. (b) 17
Prime number series. Next prime after 13 is 17.
Q10. (b) 60
D1: -4, -6, -8, -10. Next D1=-12. 72-12=60.
Q11. (d) 720
Factorial: 6!=720.
Q12. (c) 34
D1 from what we know: 10-2=8, 82-?=?, 162-82=80. Try: 2, 10, 34, 82, 162. D1: 8, 24, 48, 80. D2: 16, 24, 32. D3: 8, 8. Consistent! Missing term = 34.
Q13. (c) 39
D1: 3, 5, 7, 9. Next D1=11. 28+11=39.
Q14. (c) 24
Perfect squares: 1,4,9,16,25,36. 24 should be 25.
Q15. (c) 81
Odd positions: 3, 8, 27, ? (3^1, 2^3, 3^3, ...). Actually: 3, 8, 27 -> these look like: Alternate series: Odd: 3, 8, 27, ? Even: 4, 9, 28. Odd: 3, 8, 27 -> differences 5, 19... not clean. Try: 3^1=3, 2^3=8, 3^3=27, 4^3=64? But option is 81=3^4. Odd positions: 3, 8, 27, 81 -> x8/3, x27/8... Not clean either. Or: 3, 8, 27, 81 -> ratio ~2.67, 3.375, 3 -> approaching 3. With +1 pattern: 3, 4, 8, 9, 27, 28, 81 -> the odd positions are 3, 8, 27, 81 which are 3^1, 8, 3^3, 3^4. Actually: 3, 8, 27, 81. Ratio: 8/3, 27/8, 81/27=3. Pattern: 3, 8, 27, 81. Each: x3 doesn't work for 3->8. But +1 then x3: 3(+1)4, 8(+1)9, 27(+1)28, 81. The even terms are each odd+1. Answer: 81.
Q16. (c) 224
Geometric: r=2. 112x2=224.
Q17. (c) 63
Pattern: 2^n - 1. 2^1-1=1, 2^2-1=3, 2^3-1=7, 2^4-1=15, 2^5-1=31, 2^6-1=63.
Q18. (b) 80
D1: 5, 10, 15, 20. Next D1=25. 55+25=80.
Q19. (b) 486
Geometric: r=3. 162x3=486.
Q20. (c) 38
n^2+1: 2,5,10,17,26,37,50. 38 should be 37.
Q21. (b) 48
n^2-1: 1-1=0, 4-1=3, 9-1=8, 16-1=15, 25-1=24, 36-1=35, 49-1=48.
Q22. (a) 31
Prime numbers: 11,13,17,19,23,29,31.
Q23. (b) 60
Pattern: +2, x2, +2, x2, +2, x2. 4+2=6, 6x2=12, 12+2=14, 14x2=28, 28+2=30, 30x2=60.
Q24. (c) 3125
n^n: 1^1=1, 2^2=4, 3^3=27, 4^4=256, 5^5=3125.
Q25. (b) 15
Triangular numbers: 1,3,6,10,15,21,28. T_5=15.
Q26. (c) 34
Fibonacci-like: 13+21=34.
Q27. (b) 122
Pattern: x3-1. 1x3-1=2, 2x3-1=5, 5x3-1=14, 14x3-1=41, 41x3-1=122.
Q28. (c) 34
Powers of 2: 1,2,4,8,16,32,64. 34 should be 32.
Q29. (c) 122
Pattern: x2+1. 6x2+1=13, 13x2+2=28, 28x2+3=59, 59x2+4=122. Or: D1: 7, 15, 31, ? D1 pattern: x2+1. 31x2+1=63. Next=59+63=122.
Q30. (c) 91
These are sum of squares: 1, 1+4=5, 1+4+9=14, 1+4+9+16=30, 30+25=55, 55+36=91.
Q31. (b) 252
n^3 + n: 1+1=2, 8+4=12, 27+9=36, 64+16=80, 125+25=150, 216+36=252.
Q32. (c) 109
Pattern: each term = prev x (position). 2x1=2? No. Try: 2, 3, 6, 18, 108, 1944. Ratios: 1.5, 2, 3, 6, 18. Pattern in ratios: x(4/3), x1.5, x2, x3. Actually: 3x2=6, 6x3=18, 18x6=108, 108x18=1944. Each multiplier doubles: x2, x3, x6, x18. Hmm. Or: 2x3=6, 6x3=18, 18x6=108, 108x18=1944. 109 should be 108. Wrong: 109.
Q33. (b) 169
Squares of primes: 2^2=4, 3^2=9, 5^2=25, 7^2=49, 11^2=121, 13^2=169.
Q34. (b) 45
D1: 2, 4, 6, 8, 10. Next D1=12. 33+12=45.
Q35. (c) 240
Ratios: x1, x2, x3, x4. Next: x5. 48x5=240.
Q36. (b) 49
Pattern: x2+1. 5x2+1=11, 11x2+2=24, 24x2+1=49, 49x2+10=108... Let me recheck. D1: 6, 13, ?, ?, 113. Try: 5, 11, 24, 49, 108, 221. D1: 6, 13, 25, 59, 113. D2: 7, 12, 34, 54. Not clean. Try x2-1: 5x2+1=11, 11x2+2=24... Hmm. Actually: 5, 11, 24, 49, 108, 221. Ratios: 2.2, 2.18, 2.04, 2.2, 2.05. Close to x2. 5x2+1=11. 11x2+2=24. 24x2+1=49. 49x2+10=108. Not consistent. Maybe: D1: 6, 13, 25, 59, 113. D2: 7, 12, 34, 54. Doesn't help. Accept answer: 49.
Q37. (c) 70
D1: 4, 8, 12, 16. Next D1=20. 50+20=70.
Q38. (c) 12
Fibonacci: 1,1,2,3,5,8,13,21. 12 should be 13.
Q39. (c) 768
Geometric: r=4. 192x4=768.
Q40. (d) 67
D1: 4, 8, 16. Pattern: x2. Next D1=32. 35+32=67.
Q41. (b) 121
Squares of odd numbers: 1^2=1, 3^2=9, 5^2=25, 7^2=49, 9^2=81, 11^2=121.
Q42. (b) 138
Pattern: +1, x(something), +1, x(something). 5+1=6, 6x(7/3)=14, 14+1=15, 15x3=45, 45+1=46, 46x3=138.
Q43. (d) 768
Pattern: x1+2=5, 5x2+2=12, 12x3+2=38, 38x4+2=154, 154x5+2=772. 768 should be 772. Wrong: 768. Or: 3x2-1=5, 5x2+2=12, 12x3+2=38, 38x4+2=154, 154x5+2=772. 768 is wrong.
Q44. (d) 65
D1: 1, 2, 4, 8, 16. Geometric (x2). Next D1=32. 33+32=65.
Q45. (b) 24
Tribonacci-like: sum of previous 3. 0+1+1=2, 1+1+2=4, 1+2+4=7, 2+4+7=13, 4+7+13=24.
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