What is the common difference?
Direction: Consider the following for the two (02) items that follow :<br>The product of 5 consecutive terms of an AP is 229635. The first, second and fifth terms are in GP.
- A. 3
- B. 4
- C. 5
- D. 6 ✓
Correct Answer: D. 6
Explanation
Let the 5 terms in AP be a, a+d, a+2d, a+3d, a+4d. The 1st, 2nd, and 5th terms are in GP, so (a+d)^2 = a(a+4d) \implies a^2+2ad+d^2 = a^2+4ad \implies d^2 = 2ad \implies d = 2a. The terms become a, 3a, 5a, 7a, 9a. Their product is 945a^5 = 229635 \implies a^5 = 243 \implies a = 3. The common difference is d = 2a = 6.
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