$\bf \qquad \qquad \textit{sum of a finite geometric sequence}\\\\
S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
r=\textit{common ratio}\\
----------\\
a_1=3\\
r=\frac{1}{2}\\
n=8
\end{cases}$

$\bf S_8=3\left( \cfrac{1-\left( \frac{1}{2} \right)^8}{1-\frac{1}{2}} \right)\implies 
S_8=3\left( \cfrac{1-\frac{1^8}{2^8}}{1-\frac{1}{2}} \right)
\\\\\\
S_8=3\left( \cfrac{1-\frac{1}{256}}{\frac{1}{2}} \right)\implies S_8=3\left( \cfrac{\frac{255}{256}}{\frac{1}{2}} \right)\implies S_8=3\left( \cfrac{255}{256}\cdot \cfrac{2}{1} \right)
\\\\\\
S_8=3\left( \cfrac{255}{128} \right)\implies S_8=\cfrac{765}{128}$

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Your friend Janelle is interested in calculating her maximum heart rate before she begins her aerobics class. You tell her she c

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