Question

Find s10 for a geometric series with first term 10 and a common ratio 4

Answer 1

The sum of a geometric sequence where the first term is a1 and the common ratio is r and n is which term is
$S_{n}=\frac{a_1(1-r^n)}{1-r}$

so
given first term of 10 and common ratio 4 and n=10

$S_{10}=\frac{10(1-4^{10})}{1-4}$
$S_{10}=\frac{10(1-1048576)}{-3}$
$S_{10}=\frac{10(-1048575)}{-3}$
$S_{10}=\frac{-10485750}{-3}$
$S_{10}=3495250$

Answer 2

$\bf \qquad \qquad \textit{sum of a finite geometric sequence}\\\\ S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ ----------\\ n=10\\ r=4\\ a_1=10 \end{cases} \\\\\\ S_{10}=10\left( \cfrac{1-4^{10}}{1-4} \right)$