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?
- A. -3 ✓
- B. -2
- C. 2
- D. 3
Correct Answer: A. -3
Explanation
Terms a+4d, a+6d, a+12d are in GP. (a+6d)^2 = (a+4d)(a+12d). Expanding gives a^2 + 12ad + 36d^2 = a^2 + 16ad + 48d^2 \implies 4ad + 12d^2 = 0. So 4d(a+3d) = 0 \implies a = -3d \implies a/d = -3.
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