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=720missing 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:



  1. Take square roots of each term → get base numbers.

  2. Find the differences of consecutive bases → see the pattern.

  3. 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=720missing 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…