What is the maximum value of the sum of the numbers 36, 33, 30, 27, 24, ...?

This is an AP with first term a = 36, common difference d = -3. Sum is maximum when terms are non-negative. The terms are 36, 33, 30, ..., 3, 0. After 0, terms become negative. Number of non-negative terms: a_n = 36 + (n-1)(-3) ≥ 0 → n ≤ 13. So n = 13 terms (last term 0). Sum = (13/2)(36 + 0) = 13 × 18 = 234. Adding 0 doesn't change sum. So maximum = 234. Answer (c).