Number Series, Coding, Odd Man OutPYQ Dec 22Question 2029 of 217
All Questions

Find the missing number in the following series? 3,5,5,19,7,41,9,?,11,109\displaystyle 3, 5, 5, 19, 7, 41, 9, ?, 11, 109

Options

A71
B61
C69
D79
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Correct Answer

✅ Option a — 71

All Options:

  • A71
  • B61
  • C69
  • D79

Detailed Solution & Explanation

We are given the series: 3,5,5,19,7,41,9,?,11,109\displaystyle 3, 5, 5, 19, 7, 41, 9, ?, 11, 109
Let's split this series into two alternating sequences:
1. **Odd-positioned terms (1st, 3rd, 5th, 7th, 9th):**
- 3,5,7,9,11\displaystyle 3, 5, 7, 9, 11
- Pattern: consecutive odd numbers starting from 3\displaystyle 3 (common difference +2\displaystyle +2).
2. **Even-positioned terms (2nd, 4th, 6th, 8th, 10th):**
- 5,19,41,?,109\displaystyle 5, 19, 41, ?, 109
- Let's compute the differences between these consecutive terms:
- 19−5=14\displaystyle 19 - 5 = 14
- 41−19=22\displaystyle 41 - 19 = 22
- Notice that the differences increase by 8\displaystyle 8 each time (14+8=22\displaystyle 14 + 8 = 22).
- The next difference should be 22+8=30\displaystyle 22 + 8 = 30.
- The missing term (at the 8th position) is:
41+30=7141 + 30 = 71
- Let's check the next term in the sequence using a difference of 30+8=38\displaystyle 30 + 8 = 38:
71+38=10971 + 38 = 109
This matches the 10th term perfectly!
Hence, **Option A** is the correct answer.

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