Number Series, Coding, Odd Man OutPYQ Nov 20Question 2014 of 217
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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, ?, 75.

Options

A58
B46
C48
D54
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Correct Answer

✅ Option b — 46

All Options:

  • A58
  • B46
  • C48
  • D54

Detailed Solution & Explanation

We are given the series: 0,2,3,6,10,17,28,?,75\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 1\displaystyle 1:
an=an−1+an−2+1for n≥3a_n = a_{n-1} + a_{n-2} + 1 \quad \text{for } n \ge 3
Let's verify this pattern:
- a3=a2+a1+1  ⟹  2+0+1=3\displaystyle a_3 = a_2 + a_1 + 1 \implies 2 + 0 + 1 = 3
- a4=a3+a2+1  ⟹  3+2+1=6\displaystyle a_4 = a_3 + a_2 + 1 \implies 3 + 2 + 1 = 6
- a5=a4+a3+1  ⟹  6+3+1=10\displaystyle a_5 = a_4 + a_3 + 1 \implies 6 + 3 + 1 = 10
- a6=a5+a4+1  ⟹  10+6+1=17\displaystyle a_6 = a_5 + a_4 + 1 \implies 10 + 6 + 1 = 17
- a7=a6+a5+1  ⟹  17+10+1=28\displaystyle a_7 = a_6 + a_5 + 1 \implies 17 + 10 + 1 = 28
Following this established recurrence relation, the missing term a8\displaystyle a_8 is:
a8=a7+a6+1=28+17+1=46a_8 = a_7 + a_6 + 1 = 28 + 17 + 1 = 46
Let's verify the final term using a8=46\displaystyle a_8 = 46:
a9=a8+a7+1=46+28+1=75a_9 = a_8 + a_7 + 1 = 46 + 28 + 1 = 75
This matches the final term perfectly.
Hence, **Option B** is the correct answer.

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