Question

Which of the following is not an A.P.?

• A. \( 5, 4\frac{1}{2}, 4, 3\frac{1}{2}, \dots \)
• B. \( -1, \frac{-5}{6}, \frac{-2}{3}, \frac{-1}{2}, \dots \)
• C. \( 8, 14, 20, 26, \dots \)
• D. \( 4, 10, 15, 20, \dots \)

Hint:

Check the common difference between consecutive terms to determine if a sequence is an A.P.

Answer 1

The Correct Option is D

The common difference in an arithmetic progression (A.P.) is constant. Let's check the common difference in each option: - Option (A): Common difference is \( 4\frac{1}{2} - 5 = -\frac{1}{2} \), \( 4 - 4\frac{1}{2} = -\frac{1}{2} \), so this is an A.P. - Option (B): Common difference is \( \frac{-5}{6} - (-1) = \frac{1}{6} \), \( \frac{-2}{3} - \frac{-5}{6} = \frac{1}{6} \), so this is an A.P. - Option (C): Common difference is \( 14 - 8 = 6 \), \( 20 - 14 = 6 \), so this is an A.P. - Option (D): The common differences are \( 10 - 4 = 6 \), but \( 15 - 10 = 5 \), and \( 20 - 15 = 5 \), so this is not an A.P. Thus, the answer is \( \boxed{4, 10, 15, 20, \dots} \).