Question

What is the sum of the geometric sequence -4, 24, -144, ... if there are 7 terms?

A: -159,964
B: -26,661
C: 26,661
D: 159,963

Answer 1

`a_1=-4;\ a_2=24;\ a_3=-144;\ ...\\\\r=(a_2)/(a_1)\\\\r=(24)/(-4)=-6`

The formula of the sum of a geometric sequence:

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

We have:

`a_1=-4;\ r=-6;\ n=7`

substitute:

`S_7=(-4(1-(-6)^7))/(1-(-6))=(-4(1-(-279,936)))/(1+6)=(-4(1+279,936))/(7)\\\\=(-4\cdot279,937)/(7)=-159,964`

Answer: A: -159,964