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In any G.P. , prove that a(n-p) xxa(n+p...

In any G.P. , prove that ` a_(n-p) xxa_(n+p) = (a_(n))^(2)` .

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Let a be the first term and r be the commoon tatio
` a_(n-p) - ar^(n-p-1)`
` a_(n+p) = ar^(n + p -1)`
` therefore a_(n-p) xx a_(n+p) = a^(2) r^(n -p -1+ n + p - 1)`
` = a^(2) r^(2n-2)`
` = (ar^(n-1))^(2) = (a_(n))^(2)` .
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