If 5th, 7th and 13th terms of an AP are in GP, then what is the ratio of its first term to its common difference?

Let first term a and common difference d. Terms are a+4d, a+6d, a+12d in GP, so (a+6d)² = (a+4d)(a+12d). Expanding: a² + 12ad + 36d² = a² + 16ad + 48d². Thus -4ad - 12d² = 0, i.e., 4d(a + 3d) = 0. Since d ≠ 0, a = -3d, so a/d = -3. Hmm, that gives -3, option (a). Re-examining: -4ad = 12d², so a/d = -3. The answer is -3.