Question

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

Answer 1

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)`

Answer 2

`S_(5)=\sum\limits_(k=1)^(5){5\cdot 2^(k-1)}`