[tex]a_1=-4;\ a_2=24;\ a_3=-144;\ ...\\\\r=\dfrac{a_2}{a_1}\\\\r=\dfrac{24}{-4}=-6[/tex]
The formula of the sum of a geometric sequence:
[tex]S_n=\dfrac{a_1(1-r^n)}{1-r}[/tex]
We have:
[tex]a_1=-4;\ r=-6;\ n=7[/tex]
substitute:
[tex] S_7=\dfrac{-4(1-(-6)^7)}{1-(-6)}=\dfrac{-4(1-(-279,936))}{1+6}=\dfrac{-4(1+279,936)}{7}\\\\=\dfrac{-4\cdot279,937}{7}=-159,964 [/tex]
Answer: A: -159,964
