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Fantom [35]
3 years ago
10

What is the sum of the first 6 terms of this geometric sequence? –4, –16, –64, –256, …

Mathematics
1 answer:
MatroZZZ [7]3 years ago
6 0

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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