Which statement is correct for the three terms (a − 2b, a + b, a + 4b)?

Correct answer: They are in AP and d = 3b.

To test three symbolic terms for an arithmetic progression, calculate the two consecutive differences. The first is (a + b) − (a − 2b) = 3b. The second is (a + 4b) − (a + b) = 3b. These differences are identical for all values of a and b, so the three terms are always consecutive terms of an AP with common difference d = 3b. Therefore option A is correct. The quantity a cancels in both subtractions, so it cannot be the common difference. No extra condition such as a = b is required, and the equal differences disprove the claim that the terms are not in AP.