Number Series, Coding, Odd Man OutPYQ June 24Question 2036 of 217
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Find the missing value in the series : 51,52,60,87,151,______,492\displaystyle 51, 52, 60, 87, 151, \_\_\_\_\_\_, 492

Options

A37
B276
C317
D420
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Correct Answer

✅ Option b — 276

All Options:

  • A37
  • B276
  • C317
  • D420

Detailed Solution & Explanation

We are given the series: 51,52,60,87,151,…,492\displaystyle 51, 52, 60, 87, 151, \dots, 492
Let's compute the differences between consecutive terms:
- 52−51=1=13\displaystyle 52 - 51 = 1 = 1^3
- 60−52=8=23\displaystyle 60 - 52 = 8 = 2^3
- 87−60=27=33\displaystyle 87 - 60 = 27 = 3^3
- 151−87=64=43\displaystyle 151 - 87 = 64 = 4^3
We observe that the differences are the cubes of consecutive natural numbers (13,23,33,43\displaystyle 1^3, 2^3, 3^3, 4^3).
Following this pattern, the next difference must be 53=125\displaystyle 5^3 = 125.
Therefore, the missing term is:
151+125=276151 + 125 = 276
Let's verify the next term in the series using the next cube difference (63=216\displaystyle 6^3 = 216):
276+216=492276 + 216 = 492
This matches the final term perfectly.
Hence, **Option B** is the correct answer.

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