Question

What is the sum of the geometric sequence -1, 6, -36, ... if there are 7 terms?

A) -39,991
B) -6,665
C) 6,665
D) 39,991

Answer 1

The formula of a sum of the geometric sequence:

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

Calculate r (common ratio):

`r=(a_(n+1))/(a_n)\to r=(6)/(-1)=-6`

Substitute:

`a_1=-1,\ r=-6,\ n=7\\\\S_7=(-1(1-(-6)^7))/(1-(-6))=(-(1-(-279,936)))/(1+6)=(-(1+279,936))/(7)=-(-279,937)/(7)=-39,991`

Answer: A) -39,991