If p^th term of an AP is k, then what is the sum of p^th term, (p + q)^th term and (p − q)^th term of the AP?

Let the first term be a and common difference be d. Then p-th term = a + (p−1)d = k. The (p+q)-th term = a + (p+q−1)d and (p−q)-th term = a + (p−q−1)d. Sum = 3a + 3(p−1)d = 3[a + (p−1)d] = 3k.