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Nady [450]
4 years ago
9

How many terms are there in a geometric series if the first term is 5, the common ratio is 2, and the sum of the series is 315?

Mathematics
1 answer:
Sonja [21]4 years ago
5 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}\\
----------\\
a_1=5\\
r=2\\
S_n=315
\end{cases}
\\\\\\
315=5\left( \cfrac{1-2^n}{1-2} \right)\implies \cfrac{315}{5}=\cfrac{1-2^n}{-1}\implies 63=\cfrac{1-2^n}{-1}
\\\\\\
-63=1-2^n\implies 2^n=64\qquad \boxed{64=2^6}\qquad 2^n=2^6\implies n=6
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Answer:

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Step-by-step explanation:

Given that,

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