Question

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

Answer 1

Answer:

39,991

Step-by-step explanation:

The formula of a sum of a geometric sequence:

$S_n=\dfrac{a_1(1-r^n)}{1-r}$

We have

$a_1=1,\ a_2=-6,\ a_3=36,\ ....\\\\r=\dfrac{a_2}{a_1}\to r=\dfrac{-6}{1}=-6$

Substitute:

$a_1=1,\ n=7,\ r=-6:\\\\S_7=\dfrac{1(1-(-6)^7)}{1-(-6)^7}=\dfrac{1-(-279936)}{1+6}=\dfrac{279937}{7}=39991$