Find the missing value in the series 0, 2, 3, 6, 10, 17, 28, ?, 75 .

Option b: 46. Solution: We are given the series: 0, 2, 3, 6, 10, 17, 28, ?, 75 Let's analyze the relation between consecutive terms. We notice a tri-nacci type recurrence relation where each term is the sum of the preceding two terms plus 1 : an = an-1 + an-2 + 1 for n ≥ 3 Let's verify this pattern: - a3 = a2 + a1 + 1 2 + 0 + 1 = 3 - a4 = a3 + a2 + 1 3 + 2 + 1 = 6 - a5 = a4 + a3 + 1 6 + 3 + 1 = 10 - a6 = a5 + a4 + 1 10 + 6 + 1 = 17 - a7 = a6 + a5 + 1 17 + 10 + 1 = 28 Following this established recurrence relation, the missing term a8 is: a8 = a7 + a6 + 1 = 28 + 17 + 1 = 46 Let's verify the final term using a8 = 46 : a9 = a8 + a7 + 1 = 46 + 28 + 1 = 75 This matches the final term perfectly. Hence, Option B is the correct answer.

Find the missing value in the series $0, 2, 3, 6, 10, 17, 28, ?, 75$.

The correct answer is Option b: 46. We are given the series: $0, 2, 3, 6, 10, 17, 28, ?, 75$ Let's analyze the relation between consecutive terms. We notice a tri-nacci type recurrence relation where each term is the sum of the preceding two terms plus $1$: $$a_n = a_{n-1} + a_{n-2} + 1 \quad \text{for } n \ge 3$$ Let's verify this pattern: - $a_3 = a_2 + a_1 + 1 \implies 2 + 0 + 1 = 3$ - $a_4 = a_3 + a_2 + 1 \implies 3 + 2 + 1 = 6$ - $a_5 = a_4 + a_3 + 1 \implies 6 + 3 + 1 = 10$ - $a_6 = a_5 + a_4 + 1 \implies 10 + 6 + 1 = 17$ - $a_7 = a_6 + a_5 + 1 \implies 17 + 10 + 1 = 28$ Following this established recurrence relation, the missing term $a_8$ is: $$a_8 = a_7 + a_6 + 1 = 28 + 17 + 1 = 46$$ Let's verify the final term using $a_8 = 46$: $$a_9 = a_8 + a_7 + 1 = 46 + 28 + 1 = 75$$ This matches the final term perfectly. Hence, **Option B** is the correct answer.

Number Series, Coding and DecodingMCQPYQ Nov 20Question 2014 of 217

All Questions

Find the missing value in the series $\displaystyle 0, 2, 3, 6, 10, 17, 28, ?, 75$ .

Options

A58

B46

C48

D54

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

Correct Answer

✅ Option b — 46

All Options:

Detailed Solution & Explanation

We are given the series:

\displaystyle 0, 2, 3, 6, 10, 17, 28, ?, 75

Let's analyze the relation between consecutive terms. We notice a tri-nacci type recurrence relation where each term is the sum of the preceding two terms plus

\displaystyle 1

a_n = a_{n-1} + a_{n-2} + 1 \quad \text{for } n \ge 3

Let's verify this pattern:
-

\displaystyle a_3 = a_2 + a_1 + 1 \implies 2 + 0 + 1 = 3

\displaystyle a_4 = a_3 + a_2 + 1 \implies 3 + 2 + 1 = 6

\displaystyle a_5 = a_4 + a_3 + 1 \implies 6 + 3 + 1 = 10

\displaystyle a_6 = a_5 + a_4 + 1 \implies 10 + 6 + 1 = 17

\displaystyle a_7 = a_6 + a_5 + 1 \implies 17 + 10 + 1 = 28

Following this established recurrence relation, the missing term

\displaystyle a_8

is:

a_8 = a_7 + a_6 + 1 = 28 + 17 + 1 = 46

Let's verify the final term using

\displaystyle a_8 = 46

a_9 = a_8 + a_7 + 1 = 46 + 28 + 1 = 75

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 missing value in the series 0,2,3,6,10,17,28,?,75\displaystyle 0, 2, 3, 6, 10, 17, 28, ?, 750,2,3,6,10,17,28,?,75.