Question

How do you find `S_n` for the geometric series `a_1=243`, r=-2/3, n=5?

Answer 1

`165`

Explanation:

For the standard geometric series the sum to n terms is.

`color(red)(bar(ul(|color(white)(2/2)color(black)(S_n=(a(1-r^n))/(1-r))color(white)(2/2)|)))`

`"Here " a=a_1=243,r=-2/3" and " n=5`

`rArrS_5=(243(1-(-2/3)^5))/(1-(-2/3)`

`=(243(1+32/243))/(1+2/3)=(243+32)/(5/3)=165`