The formula of a sum of the geometric sequence:
[tex]S_n=\dfrac{a_1(1-r^n)}{1-r}[/tex]
Calculate r (common ratio):
[tex]r=\dfrac{a_{n+1}}{a_n}\to r=\dfrac{6}{-1}=-6[/tex]
Substitute:
[tex]a_1=-1,\ r=-6,\ n=7\\\\S_7=\dfrac{-1(1-(-6)^7)}{1-(-6)}=\dfrac{-(1-(-279,936))}{1+6}=\dfrac{-(1+279,936)}{7}=-\dfrac{-279,937}{7}=-39,991[/tex]
Answer: A) -39,991
