Question

Which of the given conditions holds true for p, q, r, s to be the terms of an arithmetic progression.

• A. p - q = s - r
• B. p + q + r + s = 0
• C. p + q = r + s
• D. q - p = s - r

Answer 1

The correct option is D q - p = s - r

If the difference between the second term and the first term is equal to the difference between the third term and the second term and so on, the numbers are said to be in AP.
This condition is used to verify whether the numbers are in AP or not.
If p, q, r, s are in AP then, q - p = r - q = s - r
Hence, among the given statements, q - p = s - r is the one that is used to verify whether a sequence is an AP or not.