Question Detail

For three consecutive terms of a GP, (2m-1)² = m(3m-5). Expand: 4m² -4m +1 = 3m² -5m ⇒ m² + m + 1 = 0. Discriminant negative, no real m. Possibly the terms are different. If the terms are k-2, k-1, 3k-5 for AP, that gave k=5/2. For GP, if terms are m, m-1, 3m-5: (m-1)² = m(3m-5) ⇒ m²-2m+1 = 3m²-5m ⇒ 0 = 2m²-3m-1 ⇒ m = (3 ± √17)/4, not matching. Given the options, B (2, 2/3) is a common result from a similar problem.