Question

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

Answer 1

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

Answer 2

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

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