Number Series, Coding, Odd Man OutMTP Sep 24 Series IQuestion 2079 of 217
All Questions

Find the missing value in the series: \displaystyle 51, 52, 60, 87, 151, ______. 492.

Options

A195\displaystyle 195
B276\displaystyle 276
C317\displaystyle 317
D420\displaystyle 420
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Correct Answer

✅ Option b — 276\displaystyle 276

All Options:

  • A195\displaystyle 195
  • B276\displaystyle 276
  • C317\displaystyle 317
  • D420\displaystyle 420

Detailed Solution & Explanation

To find the missing value in the series 51,52,60,87,151,?,492\displaystyle 51, 52, 60, 87, 151, ?, 492, let us analyze the differences between consecutive terms:

- 1st to 2nd term: 52−51=1=13\displaystyle 52 - 51 = 1 = 1^3
- 2nd to 3rd term: 60−52=8=23\displaystyle 60 - 52 = 8 = 2^3
- 3rd to 4th term: 87−60=27=33\displaystyle 87 - 60 = 27 = 3^3
- 4th to 5th term: 151−87=64=43\displaystyle 151 - 87 = 64 = 4^3

We observe that the difference between terms is the sequence of consecutive perfect cubes (13,23,33,43,…\displaystyle 1^3, 2^3, 3^3, 4^3, \dots).
Following this logical pattern, the next difference must be 53=125\displaystyle 5^3 = 125. We add 125\displaystyle 125 to the 5th term (151\displaystyle 151):
151+125=276151 + 125 = 276
Let us verify the final step by adding 63=216\displaystyle 6^3 = 216 to our result:
276+216=492276 + 216 = 492
This perfectly matches the last term in the sequence, mathematically proving that the missing term is 276\displaystyle 276.

Hence, **Option B** is the correct answer.

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