Find the next number in the given sequence? 11, 17, 39, 85, ?, 281, 447

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

Find the next number in the given sequence? $11, 17, 39, 85, ?, 281, 447$

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

Number Series, Coding and DecodingMCQPYQ Dec 22Question 2030 of 217

All Questions

Find the next number in the given sequence? $\displaystyle 11, 17, 39, 85, ?, 281, 447$

Options

A133

B143

C153

D163

For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option d — 163

All Options:

A133
B143
C153
D163

Detailed Solution & Explanation

We are given the sequence:

\displaystyle 11, 17, 39, 85, ?, 281, 447

Let's compute the differences between consecutive terms:
-

\displaystyle 17 - 11 = 6

\displaystyle 39 - 17 = 22

\displaystyle 85 - 39 = 46

Let's look at the differences of the differences (second differences):
-

\displaystyle 22 - 6 = 16

\displaystyle 46 - 22 = 24

The second differences are increasing by

\displaystyle 8

each time (

\displaystyle 16, 24, \dots

). Let's extend this arithmetic progression of second differences:

\displaystyle 16, 24, 32, 40, 48

.
Let's use this to calculate the next terms:
- Next first difference =

\displaystyle 46 + 32 = 78 \implies

missing term =

\displaystyle 85 + 78 = 163

.
- Next first difference =

\displaystyle 78 + 40 = 118 \implies

next term =

\displaystyle 163 + 118 = 281

. (Matches!)
- Next first difference =

\displaystyle 118 + 48 = 166 \implies

next term =

\displaystyle 281 + 166 = 447

. (Matches!)
This confirms that the missing term is

\displaystyle 163

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

About This Chapter: Number Series, Coding and Decoding

Paper

Paper 3: Quantitative Aptitude

Weightage

5 Marks

Key Topics

Number series, Coding & Decoding, Odd man out

This chapter covers Number series, Coding & Decoding, Odd man out and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 5 Marks weightage. Focus on understanding core concepts rather than memorizing.

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Find the next number in the given sequence? 11,17,39,85,?,281,447\displaystyle 11, 17, 39, 85, ?, 281, 44711,17,39,85,?,281,447