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If the pth, qth and rth terms of an arithmetic progression coincide with the corresponding terms of a geometric progression, and those terms are x, y and z respectively, then the value of x^(y−z), y^(z−x), z^(x−y) is

1. 0
2. 1
3. 2
4. None of these

Correct answer: 1

Solution

Taking logs, the exponent is (y-z)ln x+(z-x)ln y+(x-y)ln z. Writing the terms as both an AP (linear in position) and a GP (log linear in position) shows this sum is identically 0, so the product equals e^0 = 1.

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