Series Set - 2
1. What should come in place of ? : 2 12 60 240 ? 1440
Options: (a) 480 (b) 720 (c) 360 (d) 840
Why: Each term is previous term multiplied by a decreasing integer :
2 * 6 = 12
12 * 5 = 60
60 * 4=240
240 * 3=720← missing term,
720 * 2=1440
2. Find the next term from the given series. 15, 35, 77, 143, 221, ?
Option: (1) 321 (2) 323 (3) 437 (4) 187
Soln
Trick: Every term = product of two numbers with increasing gaps
Check quickly:
15 = 3 * 5,
35 = 5 * 7,
77 = 7 * 11,
143 = 11 * 13,
221 = 13 * 17
Look at the second number gap:
+2, +4, +2, +4 → alternating pattern
So next gap = +2
Last number = 17
Next = 17 + 2 = 19
Next Term = 17 × 19 = 323
Ans = 323
3. Find the next term in the series: 25, 121, 361, 1369, ?
Options: (a) 3529 (b) 1723 (c) 3481 (d) 4111
Soln:
- Recognize perfect squares: 25 = 52,121 = 112, 361 = 192,1369 = 372
- Find bases: Bases are: 5, 11, 19, 37
- Find differences between consecutive bases: 11-5 = 6, 19-11= 8, 37−19 =18
- Find next difference: Pattern of differences (as per given answer key): 6, 8, 18 → next difference = 22
- Find next base: 37 + 22 = 59
- Square the next base: 592 = 3481
Ans:(c) 3481
Short Trick:
- Take square roots of each term → get base numbers.
- Find the differences of consecutive bases → see the pattern.
- Add next difference to the last base → square it → next term.
Next term = 3481
4. 3, 8, 19, 36, 59, 90, ?
(a) 121 (b) 131 (c) 127 (d) 136
Soln
Differences: 5, 11, 17, 23, 31 → increasing by +6 each time.
Next difference : 31 + 6 = 37
Add to last number : 90 + 37 = 127
Ans = 127
5. 1, 2, 2, 4, 3, 8, 7, 10, ?
Options: A) 17 B) 15 C) 20 D) 14
Soln
Just look at odd positions: 1 (1st), 2 (3rd), 3 (5th), 7 (7th), ? ,(9th)
Pattern: 1 → 2 → 3 (each +1) , 3 → 7 (+4), So again +4
Therefore: 7 + 4 = 11
Ans = 11
6. 47, 119, 167, ? , 359, 527
(a) 279 (b) 281 (c) 283 (d) 287
Soln
After 47, every term = (prime number)² - 2
Check in:
11² - 2 = 121 - 2 = 119
13² - 2 = 169 - 2 = 167
17² - 2 = 289 - 2 = 287 ← Missing
19² - 2 = 361 - 2 = 359
23² - 2 = 529 - 2 = 527
Ans = 287
7. 79, 71, 61, 53, 43, ?
(a) 49 (b) 37 (c) 41 (d) 31
Simple pattern: subtracting alternate - 8 and - 12
79 − 8 = 71, 71 − 10 = 61, 61 − 8 = 53, 53 − 10 = 43, 43 − 6 = 37
"The series drops by −8 then −10 alternately → next drop fits only 37 in options."
Ans = 37
8. What should come in place of ? 2 12 60 240 ? 1440
Options: A) 720 B) 620 C) 500 D) 420
Ans = A) 720
Soln: Each term is previous term multiplied by a decreasing integer:
- 2×6=12, 12×5=6, 60×4=24, 240×3=720← missing term, 720×2=1440
9. 1, 2, 2, 4, 3, 8, 7, 10, ?
Options: A) 17 B) 15 C) 20 D) 14
Soln
Just look at odd positions: 1 (1st), 2 (3rd), 3 (5th), 7 (7th), ? ,(9th)
Pattern: 1 → 2 → 3 (each +1) , 3 → 7 (+4), So again +4
Therefore: 7 + 4 = 11
Ans = 11
Prime & Square/Cube Logic
Q36. 2, 3, 5, 7, 11, ___
(a) 12 (b) 13 (c) 15 (d) 17
Ans: (b) 13
Explanation: Prime numbers.
10. 1, 8, 27, 64, ___
(a) 81 (b) 125 (c) 256 (d) 100
Ans: (b) 125
Explanation: Cube numbers, 1³, 2³, 3³, 4³ → 5³ = 125
11. 4, 9, 16, 25, ___
(a) 36 (b) 49 (c) 81 (d) 100
Ans: (a) 36
Explanation: Perfect squares.
12. 6, 11, 16, 21, ___
(a) 26 (b) 28 (c) 31 (d) 32
Ans: (a) 26
Explanation: +5 each time.
13. 1, 4, 27, 256, ___
(a) 625 (b) 3125 (c) 36 (d) 81
Ans: (b) 3125
Explanation: 1 = 1¹, 4 = 2², 27 = 3³, 256 = 4⁴, Next = 5⁵ = 3125
Reverse / Trick Patterns
14. 90, 85, 80, 75, ___
(a) 72 (b) 70 (c) 65 (d) 60
Ans: (b) 70
Explanation: –5 each step.
15. 121, 144, 169, 196, ___
(a) 225 (b) 256 (c) 289 (d) 200
Ans: (b) 256
Explanation: 11², 12², 13², 14² → 15² = 225
Ans: (a) 225
16. 2, 9, 28, 65, ___
(a) 126 (b) 100 (c) 121 (d) 135
Ans: (c) 121
Explanation: n³ + 1, 1³+1 = 2, 2³+1 = 9, 3³+1 = 28, 4³+1 = 65, 5³+1 = 126
Ans: (a) 126
17. 3, 5, 9, 17, 33, ___
(a) 45 (b) 49 (c) 65 (d) 68
Ans: (c) 65
Explanation: Double and -1
3×2+? = 5 ( -1 ), 5×2+? = 9 (-1 ), 9×2+? = 17 (-1 ), 17×2+? = 33 (-1 ), 33×2-1 = 65
18. 4, 6, 10, 18, ___
(a) 34 (b) 30 (c) 20 (d) 40
Ans: (a) 34
Explanation: +2, +4, +8, +16 (doubling)
4 +2 = 6, 6 +4 = 10, 10 +8 = 18, 18 +16 = 34
Banking Exam Level
19. 14, 29, 59, 119, ___
(a) 238 (b) 239 (c) 240 (d) 245
Ans: (a) 238
Explanation: ×2 +1
14×2+1 = 29, 29×2+1 = 59, 59×2+1 = 119, 119×2+1 = 238
20. 3, 12, 36, 108, ___
(a) 324 (b) 300 (c) 280 (d) 360
Ans: (a) 324
Explanation: ×3
3×3 = 12, 12×3 = 36, 36×3 = 108, 108×3 = 324
21. 120, 60, 20, ___
(a) 15 (b) 10 (c) 5 (d) 6
Ans: (c) 5
Explanation: ÷2, ÷3, ÷4
120 ÷2 = 60, 60 ÷3 = 20, 20 ÷4 = 5
22. 2, 6, 18, 54, 162, ___
(a) 486 (b) 468 (c) 360 (d) 400
Ans: (a) 486
Explanation: ×3
23. 19, 38, 76, 152, ___
(a) 200 (b) 250 (c) 304 (d) 240
Ans: (c) 304
Explanation: ×2
19×2 = 38, 38×2 = 76, 76×2 = 152, 152×2 = 304
Alternating Series (Positive–Negative / Increasing–Decreasing)
Simple
24. 2, -4, 6, -8, 10, ?
(a) -10 (b) 12 (c) -12 (d) 8
Ans: (b) 12
Explanation: Sign alternates + numbers increase by 2:
+2, -4, +6, -8, +10, -12 but asked next in pattern of + (so 12)
25. 5, -10, 15, -20, 25, ?
(a) 30 (b) -30 (c) 35 (d) -35
Ans: (b) -30
Explanation: +5, -10, +15, -20, +25, -30
26. 1, -2, 3, -4, 5, ?
(a) -6 (b) 6 (c) 7 (d) -7
Ans: (a) -6
Explanation: Alternate sign + next number increases by 1 → -6
27. 7, -14, 21, -28, 35, ?
(a) -35 (b) 40 (c) -42 (d) 42
Ans: (c) -42
Explanation: +7, -14, +21, -28, +35, -42
28. 9, -18, 27, -36, 45, ?
(a) -45 (b) -54 (c) 54 (d) 36
Ans: (b) -54
Explanation: Pattern: multiply by 2, 3, 4, 5, 6 & alternate sign
+9, -18, +27, -36, +45, -54
Square Number Series
Simple
29. 1, 4, 9, 16, 25, ?
(a) 30 (b) 36 (c) 49 (d) 32
Ans: (b) 36
Explanation: Squares: 1², 2², 3², 4², 5², 6² = 36
30. 4, 9, 16, 25, 36, ?
(a) 42 (b) 49 (c) 64 (d) 81
Ans: (b) 49
Explanation: 2², 3², 4², 5², 6², 7² = 49
Medium
31. 49, 64, 81, 100, ?
(a) 110 (b) 120 (c) 121 (d) 90
Ans: (c) 121
Explanation: 7², 8², 9², 10², 11² = 121
32. 121, 144, 169, 196, ?
(a) 210 (b) 225 (c) 230 (d) 260
Ans: (b) 225
Explanation: 11², 12², 13², 14², 15² = 225
Tough
33. 256, 289, 324, 361, ?
(a) 380 (b) 400 (c) 420 (d) 480
Ans: (b) 400
Explanation: 16², 17², 18², 19², 20² = 400
Cube Number Series
Simple
34. 1, 8, 27, 64, 125, ?
(a) 150 (b) 216 (c) 300 (d) 225
Ans: (b) 216
Explanation: 1³, 2³, 3³, 4³, 5³, 6³ = 216
35. 8, 27, 64, 125, 216, ?
(a) 343 (b) 256 (c) 300 (d) 500
Ans: (a) 343
Explanation: 2³, 3³, 4³, 5³, 6³, 7³ = 343
Medium
36. 27, 64, 125, 216, 343, ?
(a) 400 (b) 512 (c) 490 (d) 600
Ans: (b) 512
Explanation: 3³, 4³, 5³, 6³, 7³, 8³ = 512
37. 64, 125, 216, 343, 512, ?
(a) 729 (b) 900 (c) 800 (d) 700
Answer: (a) 729
Explanation: 4³, 5³, 6³, 7³, 8³, 9³ = 729
Tough
38. 125, 216, 343, 512, 729, ?
(a) 800 (b) 900 (c) 1000 (d) 1200
Ans: (c) 1000
Explanation: 5³, 6³, 7³, 8³, 9³, 10³ = 1000
Difference of Squares
Formula: n² − (n−1)² = always odd numbers 2n − 1
Simple
39. 1, 3, 5, 7, 9, ?
(a) 10 (b) 11 (c) 12 (d) 13
Ans: (b) 11
Explanation: Difference of consecutive squares gives odd sequence.
40. 3, 5, 7, 9, 11, ?
(a) 12 (b) 13 (c) 14 (d) 15
Ans: (b) 13
Explanation: Next odd → 13
Medium
41. 15, 17, 19, 21, 23, ?
(a) 25 (b) 27 (c) 24 (d) 26
Ans: (a) 25
Explanation: All odd numbers.
42. 21, 23, 25, 27, 29, ?
(a) 30 (b) 31 (c) 33 (d) 32
Ans: (b) 31
Explanation: Next odd → 31
Tough
43. 31, 33, 35, 37, 39, ?
(a) 41 (b) 42 (c) 40 (d) 44
Ans: (a) 41
Explanation: Straight odd continuation.
44. 2, 12, 36, 80, 150, ?
(a) 250 (b) 252 (c) 270 (d) 300
Ans: (c) 270,
Pattern:
- Differences: 12−2 = 10, 36−12 = 24, 80−36 = 44, 150−80 = 70
- Second differences: 24−10 = 14, 44−24 = 20, 70−44 = 26 → increases by 6 each time
- Next difference: 70+32 = 102
- Next term: 150+102 = 252
Ans: (b) 252
45. 10, 15, 35, 110, ?
(a) 350 (b) 360 (c) 390 (d) 420
Ans: (d) 420
Pattern: 10×1+5 = 15, 15×2+5 = 35, 35×3+5 = 110, 110×4+5 = 420
Explanation: Each term roughly multiplies by a growing number to get the next term.
46. 6, 13, 27, 55, 111, ?
(a) 223 (b) 224 (c) 225 (d) 222
Ans: (a) 223, ×2 +1, ×2 +1…