Question

Find the wrong term in the following number series: \[ 6, 15, 35, 77, 143, 231 \]

• A. 143
• B. 231
• C. 35
• D. 77

Hint:

When analyzing number series, calculate the first and second differences to identify irregularities in the pattern. The term causing the irregularity is often the wrong term.

Answer 1

The Correct Option is B

Let's analyze the given series:
\[ 6, 15, 35, 77, 143, 231 \] First, calculate the differences between consecutive terms:
\[ 15 - 6 = 9, \quad 35 - 15 = 20, \quad 77 - 35 = 42, \quad 143 - 77 = 66, \quad 231 - 143 = 88 \] Next, calculate the second differences between the consecutive differences:
\[ 20 - 9 = 11, \quad 42 - 20 = 22, \quad 66 - 42 = 24, \quad 88 - 66 = 22 \] The second differences are not consistent, and there is an anomaly in the progression. The second difference between 42 and 66 is 24, while the others are 11, 22, and 22. This suggests that the term 231 is inconsistent with the expected pattern of differences. Therefore, the wrong term in the series is 231.