[tex] a_1=-4;\ a_2=-16;\ a_3=-64;\ a_4=-256;\ ...\\\\r=\dfrac{a_{n+1}}{a_n}\to r=\dfrac{a_2}{a_1}\to r=\dfrac{-16}{-4}=4 [/tex]
The formula of the sum of a geometric sequence:
[tex]S_n=a_1\cdot\dfrac{1-r^n}{1-r}[/tex]
We have:
[tex]a_1=-4;\ n=6;\ r=4[/tex]
substitute:
[tex]S_6=-4\cdot\dfrac{1-4^6}{1-4}=-4\cdot\dfrac{1-4096}{-3}=-4\cdot\dfrac{-4095}{-3}=-4\cdot1365=-5460[/tex]
Answer: C. -5460
