How do you find #S_n# for the geometric series #a_1=243#, r=-2/3, n=5?
1 Answer
Dec 19, 2016
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#
