If $x^{a} = x^{b / 2} z^{b / 2} = z^{c}$ , then $a, b, c$ are in

A . P .

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G . P .

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H . P .

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None

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Solution

The correct option is C $H . P .$
Let $x^{a} = (x z)^{b / 2} = z^{c} = t$
$\Rightarrow x = t^{1 / a}, x z = t^{2 / b}, z = t^{1 / c} ∵ x z = t^{2 / b} \Rightarrow t^{1 / a} t^{1 / c} = t^{2 / b} \Rightarrow \frac{1}{a} + \frac{1}{c} = \frac{2}{b}$

So, $a, b, c$ are in $H . P .$

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