If in a G.P. of 64 terms,the sum of all the t | vedclass

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(D) Let the $G.P.$ be $a, ar, ar^2, \ldots, ar^{63}$.The sum of all $64$ terms is $S_{64} = \frac{a(r^{64}-1)}{r-1}$.The odd terms are $a, ar^2, ar^4,

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$6$

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(D) Let the $G.P.$ be $a, ar, ar^2, \ldots, ar^{63}$.The sum of all $64$ terms is $S_{64} = \frac{a(r^{64}-1)}{r-1}$.The odd terms are $a, ar^2, ar^4, \ldots, ar^{62}$. This is a $G.P.$ with $32$ terms,first term $a$,and common ratio $r^2$.The sum of odd terms is $S_{odd} = \frac{a((r^2)^{32}-1)}{r^2-1} = \frac{a(r^{64}-1)}{r^2-1}$.Given that $S_{64} = 7 	imes S_{odd}$,we have:$\frac{a(r^{64}-1)}{r-1} = 7 	imes \frac{a(r^{64}-1)}{r^2-1}$.Assuming $r 
eq 1$ and $r^{64} 
eq 1$,we can cancel $\frac{a(r^{64}-1)}{r-1}$ from both sides:$1 = \frac{7}{r+1}$.$r+1 = 7 \Rightarrow r = 6$.

If in a $G.P.$ of $64$ terms,the sum of all the terms is $7$ times the sum of the odd terms of the $G.P.$,then the common ratio of the $G.P.$ is equal to

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