What is the summation notation for the geometric series 5 + 10 + 20 + 40 + 80?

Mathematics

2 answers:

katrin [286]3 years ago

8 0

$S_{5}=\sum\limits_{k=1}^{5}{5\cdot 2^{k-1}}$

Gekata [30.6K]3 years ago

3 0

Anyhow, the common ratio is 2, and the first term is 5 and since there are 5 terms, n = 5,

$\bf \qquad \qquad \textit{sum of a finite geometric sequence}
\\\\
S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
r=\textit{common ratio}\\
----------\\
a_1=5\\
n=5\\
r=2
\end{cases}
\\\\\\
\sum\limits_{i=1}^{5}~5\cdot 2^{i-1}$

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