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Sum of n Terms

If a1/x = b...

Question

If $a^{1 / x} = b^{1 / y} = c^{1 / z} a n d a, b, c i n G . p ., T h e n x, y, z a r e i n$

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 A A.P
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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