If (4, r, s, 31) are in an arithmetic progression, what is the value of s−r?

Correct answer: 9

In a four-term arithmetic progression, the change from the first term to the fourth term covers three equal common differences. Let that common difference be d. The fourth term is therefore 4 + 3d, and the given fourth term gives 4 + 3d = 31. Hence 3d = 27 and d = 9. Since r is the second term and s is the third term, the difference s − r is exactly one common difference, so s − r = 9. A full check gives the sequence 4, 13, 22, 31, where every adjacent difference is 9. Therefore option C is correct. The value 27 is the total change from the first to the fourth term, not the difference between adjacent terms; confusing these quantities is the main likely error.