If $a, b, c$ , are in AP then $x^{a}, x^{b}, x^{c}$ will be in

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Solution

The correct option is A GP
Given:
$a, b, c$ are in A.P.
$∴ 2 b = a + c$
Taking $x$ to the power on both sides:
$∴ x^{2 b} = x^{a + c}$
$\Rightarrow (x^{b})^{2} = x^{a} x^{c}$
$∴ x^{a}, x^{b}, x^{c}$ are in G.P.
Hence, the answer is GP.

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