Question

What is the sum of the geometric series in which a1 = −5, r = 3, and an = −405?

a: -1220
b:605
c:-15
d:-605

Answer 1

`a_1=-5;\ r=3;\ a_n=-405\\\\a_n=a_1r^(n-1)\\\\subtitute\\\\-5\cdot3^(n-1)=-405\ \ \ |divide\ both\ sides\ by\ (-5)\\\\3^(n-1)=81\\\\3^(n-1)=3^4\iff n-1=4\to n=5\\\\S_n=(a_1(1-r^n))/(1-r)\\\\S_5=(-5(1-3^5))/(1-3)=(-5(1-243))/(-2)=(5\cdot(-242))/(2)=5\cdot(-121)=-605\\\\\\Answer:\boxed{S_5=-605}`