Question

Find out the wrong number in the FOLLOWING series. 2, 5, 10, 17, 26, 38, 50, 65

• A. 50
• B. 65
• C. 26
• D. 38

Hint:

When you see numbers in a series that are close to perfect squares (like 2, 5, 10, 17), a good first step is to test the patterns \( n^2+1 \), \( n^2-1 \), or \( n^2+n \). This can often reveal the underlying logic of the series very quickly.

Answer 1

The Correct Option is D

Let's analyze the pattern in the series. One common pattern is \( n^2 + 1 \) or \( n^2 - 1 \). Let's test the pattern \( n^2 + 1 \), starting with n=1. \[\begin{array}{rl} \bullet & \text{\( 1^2 + 1 = 2 \) (Matches)} \\ \bullet & \text{\( 2^2 + 1 = 5 \) (Matches)} \\ \bullet & \text{\( 3^2 + 1 = 10 \) (Matches)} \\ \bullet & \text{\( 4^2 + 1 = 17 \) (Matches)} \\ \bullet & \text{\( 5^2 + 1 = 26 \) (Matches)} \\ \bullet & \text{\( 6^2 + 1 = 37 \). The series has 38. This is a mismatch.} \\ \bullet & \text{Let's check the next terms based on the pattern:} \\ \bullet & \text{\( 7^2 + 1 = 50 \) (Matches)} \\ \bullet & \text{\( 8^2 + 1 = 65 \) (Matches)} \\ \end{array}\] The number that breaks the consistent pattern of \( n^2 + 1 \) is 38. It should have been 37. Therefore, 38 is the wrong number in the series.