Find the missing term in each of the following series: $6, 13, 25, 51, 101.$

The correct answer is Option c: $203$. To find the missing term of the series $6, 13, 25, 51, 101, ?$, we analyze the relation between consecutive terms: - 1st term to 2nd term: $6 \times 2 + 1 = 13$ - 2nd term to 3rd term: $13 \times 2 - 1 = 25$ - 3rd term to 4th term: $25 \times 2 + 1 = 51$ - 4th term to 5th term: $51 \times 2 - 1 = 101$ We observe an alternating pattern where each term is multiplied by $2$ and then we alternately add $1$ and subtract $1$ ($+1, -1, +1, -1, \dots$). Following this pattern, the next term must be computed by multiplying the 5th term by $2$ and adding $1$: $$101 \times 2 + 1 = 202 + 1 = 203$$ Hence, **Option C** is the correct answer.

Number Series, Coding and DecodingMCQMTP Dec 22 - Series IQuestion 2062 of 217

All Questions

Find the missing term in each of the following series: $\displaystyle 6, 13, 25, 51, 101.$

Options

\displaystyle 201

\displaystyle 205

\displaystyle 203

\displaystyle 207

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Correct Answer

✅ Option c — $\displaystyle 203$

All Options:

A $\displaystyle 201$
B $\displaystyle 205$
C $\displaystyle 203$
D $\displaystyle 207$

Detailed Solution & Explanation

To find the missing term of the series

\displaystyle 6, 13, 25, 51, 101, ?

, we analyze the relation between consecutive terms:

- 1st term to 2nd term:

\displaystyle 6 \times 2 + 1 = 13

- 2nd term to 3rd term:

\displaystyle 13 \times 2 - 1 = 25

- 3rd term to 4th term:

\displaystyle 25 \times 2 + 1 = 51

- 4th term to 5th term:

\displaystyle 51 \times 2 - 1 = 101

We observe an alternating pattern where each term is multiplied by

\displaystyle 2

and then we alternately add

\displaystyle 1

and subtract

\displaystyle 1

(

\displaystyle +1, -1, +1, -1, \dots

).
Following this pattern, the next term must be computed by multiplying the 5th term by

\displaystyle 2

and adding

\displaystyle 1

101 \times 2 + 1 = 202 + 1 = 203

Hence, **Option C** 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 missing term in each of the following series: 6,13,25,51,101.\displaystyle 6, 13, 25, 51, 101.6,13,25,51,101.