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Question

Let a, b, c be a three-term arithmetic series where all the terms are positive, such that abc = 64. Find the smallest possible value of b.

Accepted Answer

By AM-GM, a + b + c3 [3]abc = [3]64 = 4.Since a, b, c form an arithmetic series, a + b + c3 = b, so b 4. Equality occurs when a = b = c = 4, so the smallest possible value of b is 4.