If the fourth seventh and tenth terms of a $G . P$ are $x, y, z$ respectively, prove that $x, y, z$ are in $G . P$

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Solution

We have,
$\begin{matrix} a r^{3} = x a r^{6} = y a^{9} = z G e o m e t r i c m e a n s o f G . P . i s b^{2} = a c a r^{6} = \sqrt{a r^{3} \cdot a r^{9}} = \sqrt{a^{2} r^{12}} = \sqrt{{(a r^{6})}^{2}} = a r^{6} y^{2} = x z x, y, x a r e i n G . P \end{matrix}$

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