Question

What is the sum of the first 6 terms of this geometric sequence? –4, –16, –64, –256, …

A. –1024
B. –4096
C. –5460
D. –5476

Answer 1

`a_1=-4;\ a_2=-16;\ a_3=-64;\ a_4=-256;\ ...\\\\r=(a_(n+1))/(a_n)\to r=(a_2)/(a_1)\to r=(-16)/(-4)=4`

The formula of the sum of a geometric sequence:

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

We have:

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

substitute:

`S_6=-4\cdot(1-4^6)/(1-4)=-4\cdot(1-4096)/(-3)=-4\cdot(-4095)/(-3)=-4\cdot1365=-5460`

Answer: C. -5460