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15. Given a G.P. with a = 729 and $7 ^{th}$ term 64, determine $s_7$

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Given a G.P. with a = 729 and $7 ^{th}$ term 64.

$a_n=a.r^{n-1}$

$\Rightarrow 64=729.r^{7-1}$

$\Rightarrow r^6=\frac{64}{729}$

$\Rightarrow r^6=\left ( \frac{2}{3} \right )^6$

$\Rightarrow r=\frac{2}{3}$

$S_n=\frac{a(1-r^n)}{1-r}$

$S_7=\frac{729(1-\left ( \frac{2}{3} \right )^7)}{1-\frac{2}{3}}$

$S_7=\frac{729(1-\left ( \frac{2}{3} \right )^7)}{\frac{1}{3}}$

$S_7=3\times 729 \left ( \frac{3^7-2^7}{3^7} \right )$

$S_7= \left ( 3^7-2^7 \right )$

$S_7= 2187-128$

$S_7= 2059$ (Answer)

Posted by

seema garhwal

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