Number Series, Coding, Odd Man OutMTP June 24 Series IIIQuestion 2078 of 217
All Questions

Find next term of the series 4,9,16,25,36,49,?\displaystyle 4, 9, 16, 25, 36, 49, ?

Options

A1\displaystyle 1
B9\displaystyle 9
C20\displaystyle 20
D64\displaystyle 64
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Correct Answer

✅ Option d — 64\displaystyle 64

All Options:

  • A1\displaystyle 1
  • B9\displaystyle 9
  • C20\displaystyle 20
  • D64\displaystyle 64

Detailed Solution & Explanation

To find the next term of the series 4,9,16,25,36,49,?\displaystyle 4, 9, 16, 25, 36, 49, ?, let us analyze the mathematical definition of each term:

We observe that the sequence is composed of consecutive perfect squares starting from 22\displaystyle 2^2:
- 1st term: 22=4\displaystyle 2^2 = 4
- 2nd term: 32=9\displaystyle 3^2 = 9
- 3rd term: 42=16\displaystyle 4^2 = 16
- 4th term: 52=25\displaystyle 5^2 = 25
- 5th term: 62=36\displaystyle 6^2 = 36
- 6th term: 72=49\displaystyle 7^2 = 49

Following this clear and unique mathematical progression, the next term must be:
- 7th term: 82=64\displaystyle 8^2 = 64

Therefore, the mathematically correct answer is **64\displaystyle 64**, which corresponds to **Option D**.

*Note on Answer Key Discrepancy:* The textbook answer key lists **Option C** (20\displaystyle 20) as the correct answer. However, 20\displaystyle 20 is completely unrelated to any mathematical pattern in the sequence, whereas 64\displaystyle 64 is the unique, mathematically proven next term (82\displaystyle 8^2). This is a clear typographical error in the official answer key, and the correct option is **Option D**.

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

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