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If a, b, c form an arithmetic progression with common difference d, then the numbers e^(1/c), e^(b/ac), and e^(1/a) are in:

1. G.P. with common ratio e^d
2. G.P. with common ratio e^(1/d)
3. G.P. with common ratio e^(d/(b²-d²))
4. A.P.

Correct answer: G.P. with common ratio e^(d/(b²-d²))

Solution

The numbers e^(1/c), e^(b/ac), and e^(1/a) form a geometric progression because their ratios are constant, specifically e^(d/(b²-d²)), which arises from the relationships defined by the arithmetic progression of a, b, and c.

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