Number Series, Coding, Odd Man OutPYQ Nov 20Question 2017 of 217
All Questions

Find the next term 1,5,21,57,______\displaystyle 1, 5, 21, 57, \_\_\_\_\_\_.

Options

A105
B138
C121
D101
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Correct Answer

✅ Option c — 121

All Options:

  • A105
  • B138
  • C121
  • D101

Detailed Solution & Explanation

We are given the series: 1,5,21,57,…\displaystyle 1, 5, 21, 57, \dots
Let's compute the differences between consecutive terms:
- 5−1=4=22\displaystyle 5 - 1 = 4 = 2^2
- 21−5=16=42\displaystyle 21 - 5 = 16 = 4^2
- 57−21=36=62\displaystyle 57 - 21 = 36 = 6^2
We observe that the differences are the squares of consecutive even numbers (22,42,62\displaystyle 2^2, 4^2, 6^2).
Following this pattern, the next difference must be the square of the next even number, which is 82=64\displaystyle 8^2 = 64.
Therefore, the next term is:
57+64=12157 + 64 = 121
Hence, **Option C** is the correct answer.

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