Respuesta :
[tex]\bf \qquad \qquad \textit{sum of a finite geometric sequence} \\\\ S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf \displaystyle\sum \limits_{n=1}^{7}\stackrel{\stackrel{a_1}{\downarrow }}{2}(\stackrel{\stackrel{r}{\downarrow }}{-2})^{n-1}\implies S_7=2\left( \cfrac{1-(-2)^7}{1-(-2)} \right)\implies S_7=2\left( \cfrac{1-(-128)}{1+2} \right) \\\\\\ S_7=2\left( \cfrac{1+128}{1+2} \right)\implies S_7=2\left( \cfrac{129}{3} \right)\implies S_7=2(43)\implies S_7=86[/tex]
Answer: 86
Step-by-step explanation:
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