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valina [46]
3 years ago
5

Determine the sum of the first 9 terms in the geometric series where r= -0.25 and a1= 256.

Mathematics
2 answers:
Damm [24]3 years ago
4 0

\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}

\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

NikAS [45]3 years ago
3 0

Answer:

C). 204.8

Step-by-step explanation:

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