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)=(a_1(1-r^n))/(1-r)`

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


`S_(10)=(10(1-4^(10)))/(1-4)`

`S_(10)=(10(1-1048576))/(-3)`

`S_(10)=(10(-1048575))/(-3)`

`S_(10)=(-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)`