Question

Find the missing number in the series: 5, 11, 24, 51, ?, 213

• A. 102
• B. 106
• C. 104
• D. 108

Hint:

In number series, analyze first-level and second-level differences; look for multiplication or consistent operations.

Answer 1

The Correct Option is B

To resolve the problem, we must identify the pattern in the number sequence: 5, 11, 24, 51, ?, 213.

1. Pattern Observation:
Examine the differences between consecutive numbers:

11 - 5 = 6
24 - 11 = 13
51 - 24 = 27
? - 51 = ?
213 - ? = ?

2. Difference Analysis:
Analyze the pattern within these differences:

6, 13, 27
What is the next difference? Let's investigate:
From 6 to 13: +7
From 13 to 27: +14
The increments (7, 14, ...) appear to be doubling.
Therefore, the next difference is 27 + 28 = 55.

3. Missing Number Calculation:
Add the calculated next difference to the last known number:

51 + 55 = 106

4. Pattern Confirmation:
The final term is 213. Verify the difference between 213 and the calculated number (106):

213 - 106 = 107
The preceding difference was 55. If the doubling pattern continues:
The next difference should be 55 + 52 = 107, which matches the calculated difference!

Conclusion:
The missing value in the sequence is 106.