If x, G_1, G_2, y are the consecutive terms o | vedclass

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(C) Given that $x, G_1, G_2, y$ are in a Geometric Progression $(G.P.)$.Let the common ratio of the $G.P.$ be $r$.Then,$G_1 = xr$,$G_2 = xr^2$,and $y

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$xy$

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(C) Given that $x, G_1, G_2, y$ are in a Geometric Progression $(G.P.)$.Let the common ratio of the $G.P.$ be $r$.Then,$G_1 = xr$,$G_2 = xr^2$,and $y = xr^3$.From the last term,we have $r^3 = y/x$,so $r = (y/x)^{1/3}$.Now,the product $G_1 G_2 = (xr)(xr^2) = x^2 r^3$.Substituting $r^3 = y/x$ into the expression:$G_1 G_2 = x^2 (y/x) = xy$.Alternatively,in any $G.P.$,the product of terms equidistant from the beginning and the end is constant and equal to the product of the first and last terms. Thus,$G_1 G_2 = x \cdot y$.

If $x, G_1, G_2, y$ are the consecutive terms of a $G.P.$,then the value of $G_1 G_2$ will be

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