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 solve the problem, we need to identify the pattern in the number series: 5, 11, 24, 51, ?, 213.

1. Observing the Pattern:
Let’s examine the differences between consecutive terms:

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

2. Analyzing the Differences:
Now, look at the pattern in the differences:

6, 13, 27
Next difference? Let’s analyze this:
From 6 to 13: +7
From 13 to 27: +14
Pattern of adding (7, 14, ...), appears to double.
So, next difference = 27 + 28 = 55

3. Calculating the Missing Number:
Now add the next difference to the last known number:

51 + 55 = 106

4. Confirming the Pattern:
Final term is 213. Check the difference between 213 and 106:

213 − 106 = 107
Previous difference was 55; if pattern of doubling continues:
Next difference = 55 + 52 = 107 → which matches!

Final Answer:
The missing number in the series is 106.