Number Series, Coding, Odd Man OutPYQ Jun 23Question 2031 of 217
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The number in place of question mark in: 7,26,63,124,215,?,511\displaystyle 7, 26, 63, 124, 215, ?, 511 is

Options

A342
B343
C441
D421
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Correct Answer

✅ Option a — 342

All Options:

  • A342
  • B343
  • C441
  • D421

Detailed Solution & Explanation

We are given the series: 7,26,63,124,215,?,511\displaystyle 7, 26, 63, 124, 215, ?, 511
Let's express each term in relation to perfect cubes:
- 7=23−1\displaystyle 7 = 2^3 - 1
- 26=33−1\displaystyle 26 = 3^3 - 1
- 63=43−1\displaystyle 63 = 4^3 - 1
- 124=53−1\displaystyle 124 = 5^3 - 1
- 215=63−1\displaystyle 215 = 6^3 - 1
The terms follow the pattern n3−1\displaystyle n^3 - 1 for consecutive integers n\displaystyle n starting from 2\displaystyle 2.
Therefore, the missing term is 73−1\displaystyle 7^3 - 1:
73−1=343−1=3427^3 - 1 = 343 - 1 = 342
Let's verify the next term in the series:
83−1=512−1=5118^3 - 1 = 512 - 1 = 511
This matches the final term perfectly.
Hence, **Option A** is the correct answer.

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