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If $a^{1 / x}=b^{1 / y}=c^{1 / z}$ and ${ }^{a, b, c}$ are in G.P., then $x, y, z$ will be in
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The correct answer is:
A.P.
Let $a^{1 / x}=b^{1 / y}=c^{1 / z}=k \Rightarrow a=k^x, b=k^y, c=k^z$
Now, $a, b, c$ are in G.P.
$\Rightarrow b^2=a c \Rightarrow k^{2 y}=k^x \cdot k^z=k^{x+z} \Rightarrow 2 y=x+z$
$\Rightarrow \quad x, y, z$ are in A.P.
Now, $a, b, c$ are in G.P.
$\Rightarrow b^2=a c \Rightarrow k^{2 y}=k^x \cdot k^z=k^{x+z} \Rightarrow 2 y=x+z$
$\Rightarrow \quad x, y, z$ are in A.P.
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