Question

What is the next number in the series given below?
\(5, 6, 8, 14, 38, 158, ?\)

• A. 428
• B. 528
• C. 628
• D. 828

Answer 1

The Correct Option is D

Finding the Next Number in the Series

Given the series: 5, 6, 8, 14, 38, 158, ... 

Step-by-Step Analysis

1. Calculate the Differences Between Consecutive Terms:

• 6 - 5 = 1
• 8 - 6 = 2
• 14 - 8 = 6
• 38 - 14 = 24
• 158 - 38 = 120

The differences are: 1, 2, 6, 24, 120.

2. Identifying the Pattern:

Observing the pattern in the differences, each term is multiplied by an increasing integer:

• 1 × 2 = 2
• 2 × 3 = 6
• 6 × 4 = 24
• 24 × 5 = 120

Following this pattern, the next difference should be:

120 × 6 = 720

3. Finding the Next Number:

Adding this difference to the last term in the series:

158 + 720 = 878

Final Answer:

The next number in the series is 878 (Option D).