Find the next terms- 3, 7, 15, 31, ?, 127

Option b: 63. Solution: We are given the series: 3, 7, 15, 31, ?, 127 Let's express each term in relation to powers of 2 : - 3 = 22 - 1 - 7 = 23 - 1 - 15 = 24 - 1 - 31 = 25 - 1 The terms follow the pattern 2k - 1 for consecutive integers k . Therefore, the missing term must be 26 - 1 : 26 - 1 = 64 - 1 = 63 Let's verify the next term in the series: 27 - 1 = 128 - 1 = 127 This matches the final term perfectly. Hence, Option B is the correct answer.

Find the next terms- $3, 7, 15, 31, ?, 127$

The correct answer is Option b: 63. We are given the series: $3, 7, 15, 31, ?, 127$ Let's express each term in relation to powers of $2$: - $3 = 2^2 - 1$ - $7 = 2^3 - 1$ - $15 = 2^4 - 1$ - $31 = 2^5 - 1$ The terms follow the pattern $2^k - 1$ for consecutive integers $k$. Therefore, the missing term must be $2^6 - 1$: $$2^6 - 1 = 64 - 1 = 63$$ Let's verify the next term in the series: $$2^7 - 1 = 128 - 1 = 127$$ This matches the final term perfectly. Hence, **Option B** is the correct answer.

Number Series, Coding and DecodingMCQPYQ June 22Question 2027 of 217

All Questions

Find the next terms- $\displaystyle 3, 7, 15, 31, ?, 127$

Options

A62

B63

C64

D65

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

Correct Answer

✅ Option b — 63

All Options:

Detailed Solution & Explanation

We are given the series:

\displaystyle 3, 7, 15, 31, ?, 127

Let's express each term in relation to powers of

\displaystyle 2

:
-

\displaystyle 3 = 2^2 - 1

\displaystyle 7 = 2^3 - 1

\displaystyle 15 = 2^4 - 1

\displaystyle 31 = 2^5 - 1

The terms follow the pattern

\displaystyle 2^k - 1

for consecutive integers

\displaystyle k

.
Therefore, the missing term must be

\displaystyle 2^6 - 1

2^6 - 1 = 64 - 1 = 63

Let's verify the next term in the series:

2^7 - 1 = 128 - 1 = 127

This matches the final term perfectly.
Hence, **Option B** 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 terms- 3,7,15,31,?,127\displaystyle 3, 7, 15, 31, ?, 1273,7,15,31,?,127