If a, b, c are in G.P. and $a^{1 / x} = b^{1 / y} = c^{1 / z}$ , then $x, y, z$ are in

A.P.

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G.P.

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H.P.

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Cannot be determined

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Solution

The correct option is A A.P.
We have,
$a^{1 / x} = b^{1 / y} = c^{1 / z} = λ$
$a = λ^{x}, b = λ^{y}, c = λ^{z}$
Now, $a, b, c$ are in G.P.
$b^{2} = a c$
$(λ^{y})^{2} = λ^{x} \times λ^{z} = λ^{x + z}$
$2 y = x + z$
$x, y, z$ are in A.P.

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