Find the sum of the first 7 terms of a GP, wh | vedclass

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(C) Given: First term $a = 1024$ and common ratio $r = \frac{1}{2}$.The formula for the sum of the first $n$ terms of a $GP$ is $S_n = \frac{a(1 - r^n

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$2032$

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(C) Given: First term $a = 1024$ and common ratio $r = \frac{1}{2}$.The formula for the sum of the first $n$ terms of a $GP$ is $S_n = \frac{a(1 - r^n)}{1 - r}$ for $r Substituting the values for $n = 7$:$S_7 = \frac{1024(1 - (\frac{1}{2})^7)}{1 - \frac{1}{2}}$$S_7 = \frac{1024(1 - \frac{1}{128})}{\frac{1}{2}}$$S_7 = 1024 	imes (\frac{127}{128}) 	imes 2$$S_7 = 8 	imes 127 	imes 2 = 16 	imes 127 = 2032$.

Find the sum of the first $7$ terms of a $GP,$ whose first term is $1024$ and the common ratio is $\frac{1}{2}$.

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