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Sum of Infinite Terms of a GP

If 1,x,y,z,2 ...

Question

If 1,x,y,z,2 are in G.P then xyz =

A

2 \sqrt{2}

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B

4

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C

8

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D

none of these

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Solution

The correct option is A $2 \sqrt{2}$
$1, x, y, z, 2$ are in $G . P$
Let Common ration be $r ⟹ r^{4} = 2$
$x y z = r (r^{2}) (r^{3}) = r^{6} = 2 \sqrt{2}$

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