Question

Find the sum:

$\sum _{i=1}^{10}5{\left(2\right)}^i$

Short answer

The sum is equal to$10230$

Step-by-step solution

Step 1. Given information

It is given that$\sum _{i=1}^{10}5{\left(2\right)}^i$.

Step 2. Find the sum.

Consider $\sum _{i=1}^{10}5{\left(2\right)}^i$

Let $a,r$denote the first term and common ratio respectively.

role="math" localid="1645371460934" $\begin{array}{rcl}a& =& 5{\left(2\right)}^1\\ & =& 10\\ r& =& \frac{5{\left(2\right)}^{i+1}}{5{\left(2\right)}^i}\\ & =& 2\end{array}$

So,

$S_n=\frac{a\left(1-r^n\right)}{1-r}$where $S_n$is the sum.

$\begin{array}{rcl}{S}_{10}& =& \frac{10\left(1-2^{10}\right)}{1-2}\\ & =& -10\left(1-1024\right)\\ & =& 10230\end{array}$