If the pth term of an AP is q and the qth term is p, where p and q are distinct positive integers, then the (p+q)th term is:
Correct: A
For an AP with first term a and common difference d: a_p = a + (p-1)d = q ...(1) and a_q = a + (q-1)d = p ...(2). Subtract (2) from (1): (p-1)d - (q-1)d = q - p → (p-q)d = q-p → (p-q)d = -(p-q) → d = -1 (since p≠q). From (1): a + (p-1)(-1) = q → a - p + 1 = q → a = p + q - 1. Now the (p+q)th term: a_{p+q} = a + (p+q-1)d = (p+q-1) + (p+q-1)(-1) = (p+q-1) - (p+q-1) = 0. Therefore, the (p+q)th term is 0.