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

True

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False

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Solution

The correct option is A True
Let
$a^{1 / x} = b^{1 / y} = c^{1 / z} = k$

So,
$a = k^{x}, b = k^{y}, c = k^{z}$

Since,
$a, b, c$ are in $G . P$

So,
$b^{2} = a c$

Now,
$k^{2 y} = k^{x} . k^{z}$
$k^{2 y} = k^{x + z}$

Therefore,
$2 y = x + z$

Hence, $x, y, z$ are in $A . P$

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