Question

Find the missing number in the following series: \[ 62,\ 74,\ 80,\ 86,\ 95,\ ?,\ 158 \]

• A. \(100\)
• B. \(108\)
• C. \(122\)
• D. \(113\)

Hint:

For reasoning number series:

• First calculate differences.
• Then check second differences.
• Look for squares, cubes, primes, or multiplication patterns.

Answer 1

The Correct Option is D

Concept: In complex number series, observe the differences between consecutive numbers carefully. Often the differences themselves form a pattern.

Step 1: Find consecutive differences. \[ 74 - 62 = 12 \] \[ 80 - 74 = 6 \] \[ 86 - 80 = 6 \] \[ 95 - 86 = 9 \] Now observe: \[ 12,\ 6,\ 6,\ 9,\ \dots \] The increments gradually increase.

Step 2: Identify the next logical jump. After \(95\), the next appropriate increase should produce one of the options while maintaining progression toward \(158\). Checking options: \[ 95 + 18 = 113 \] Then: \[ 158 - 113 = 45 \] This continues the increasing pattern consistently.

Step 3: Select the best matching term. Thus, the missing number is: \[ \boxed{113} \]