Question

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

Answer 1

39,991

Explanation:

The formula of a sum of a geometric sequence:

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

We have

`a_1=1,\ a_2=-6,\ a_3=36,\ ....\\\\r=(a_2)/(a_1)\to r=(-6)/(1)=-6`

Substitute:

`a_1=1,\ n=7,\ r=-6:\\\\S_7=(1(1-(-6)^7))/(1-(-6)^7)=(1-(-279936))/(1+6)=(279937)/(7)=39991`