Given a G.P. with a=729 and 7^{text {th }} te | vedclass

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Question

$a=729 a_{7}=64$

Let $r$ be the common ratio of the $G.P.$ It is known that,

$a_{n}=a r^{n-1}$

$a_{7}=a r^{7-1}=(729) r^{6}$

$\Rightarrow

Vedclass · Accepted Answer

$2059$

Vedclass · Answer

$a=729 a_{7}=64$

Let $r$ be the common ratio of the $G.P.$ It is known that,

$a_{n}=a r^{n-1}$

$a_{7}=a r^{7-1}=(729) r^{6}$

$\Rightarrow 64=729 r^{6}$

$\Rightarrow r^{6}=\left(\frac{2}{3}ight)^{6}$

$\Rightarrow r=\frac{2}{3}$

Also, it is known that,

$S_{n}=\frac{a\left(1-r^{n}ight)}{1-r}$

$	herefore S_{7}=\frac{729\left(1-\left(\frac{2}{3}ight)^{7}ight)}{1-\frac{2}{3}}$

$=3 	imes 729\left[1-\left(\frac{2}{3}ight)^{7}ight]$

$=(3)^{7}\left[\frac{(3)^{7}-(2)^{7}}{(3)^{7}}ight]$

$=(3)^{7}-(2)^{7}$

$=2187-128$

$=2059$

Given a $G.P.$ with $a=729$ and $7^{\text {th }}$ term $64,$ determine $S_{7}$

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