[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}\\
----------\\
r=-0.25\\
a_1=256\\
n=9
\end{cases} [/tex]
[tex] \bf S_9=256\left(\cfrac{1-(-0.25)^9}{1-(-0.25)} \right)\implies S_9=256\left( \cfrac{1+0.25^9}{1+0.25} \right)
\\\\\\
S_9=256\left( \cfrac{52429}{65536}\right)\implies S_9=\cfrac{52429}{256}\implies S_9=204.80078125 [/tex]
Answer:
C). 204.8
Step-by-step explanation:
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