Verified Answer :

gmany

\(a_1=-4;\ a_2=-16;\ a_3=-64;\ a_4=-256;\ ...\\\\r=\dfrac{a_{n+1}}{a_n}\to r=\dfrac{a_2}{a_1}\to r=\dfrac{-16}{-4}=4\)

The formula of the sum of a geometric sequence:

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

We have:

\(a_1=-4;\ n=6;\ r=4\)

substitute:

\(S_6=-4\cdot\dfrac{1-4^6}{1-4}=-4\cdot\dfrac{1-4096}{-3}=-4\cdot\dfrac{-4095}{-3}=-4\cdot1365=-5460\)

Answer: C. -5460

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