Question

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

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

Hint:

An arithmetic progression (A.P.) must have a common difference \( d \) between consecutive terms.

Answer 1

The Correct Option is D

An arithmetic progression (A.P.) has a constant common difference \( d \). Checking each sequence:
- (A) \( d = -\frac{1}{2} \) (constant)
- (B) \( d = \frac{1}{6} \) (constant)
- (C) \( d = 6 \) (constant)
- (D) Differences: \( 10 - 4 = 6, 15 - 10 = 5, 20 - 15 = 5 \) (not constant)
Thus, (D) is not an A.P.