Answer:
39,991
Step-by-step explanation:
The formula of a sum of a geometric sequence:
[tex]S_n=\dfrac{a_1(1-r^n)}{1-r}[/tex]
We have
[tex]a_1=1,\ a_2=-6,\ a_3=36,\ ....\\\\r=\dfrac{a_2}{a_1}\to r=\dfrac{-6}{1}=-6[/tex]
Substitute:
[tex]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[/tex]
