Number Series, Coding, Odd Man OutPYQ Dec 22Question 2030 of 217
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Find the next number in the given sequence? 11,17,39,85,?,281,447\displaystyle 11, 17, 39, 85, ?, 281, 447

Options

A133
B143
C153
D163
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Correct Answer

✅ Option d — 163

All Options:

  • A133
  • B143
  • C153
  • D163

Detailed Solution & Explanation

We are given the sequence: 11,17,39,85,?,281,447\displaystyle 11, 17, 39, 85, ?, 281, 447
Let's compute the differences between consecutive terms:
- 17−11=6\displaystyle 17 - 11 = 6
- 39−17=22\displaystyle 39 - 17 = 22
- 85−39=46\displaystyle 85 - 39 = 46
Let's look at the differences of the differences (second differences):
- 22−6=16\displaystyle 22 - 6 = 16
- 46−22=24\displaystyle 46 - 22 = 24
The second differences are increasing by 8\displaystyle 8 each time (16,24,…\displaystyle 16, 24, \dots). Let's extend this arithmetic progression of second differences: 16,24,32,40,48\displaystyle 16, 24, 32, 40, 48.
Let's use this to calculate the next terms:
- Next first difference = 46+32=78  ⟹  \displaystyle 46 + 32 = 78 \implies missing term = 85+78=163\displaystyle 85 + 78 = 163.
- Next first difference = 78+40=118  ⟹  \displaystyle 78 + 40 = 118 \implies next term = 163+118=281\displaystyle 163 + 118 = 281. (Matches!)
- Next first difference = 118+48=166  ⟹  \displaystyle 118 + 48 = 166 \implies next term = 281+166=447\displaystyle 281 + 166 = 447. (Matches!)
This confirms that the missing term is 163\displaystyle 163.
Hence, **Option D** is the correct answer.

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