Mathematics: What is the sum of the first 6 terms of this geometric sequence? –4, –16, –64, –256, …a.–1024b.–4096c.–5460d.–5476?

What is the sum of the first 6 terms of this geometric

Ответ:

tatibean26

03.01.2022

$\text{Sum to n terms of geometric series: } S_n = \frac{a(r^{n} - 1)}{r - 1}}, r \neq 1$

We know that a is equal to the first term, r represents the common ratio, and n represents the number of terms.

a = -4
n = 6

To find r:
$\frac{-16}{-4} = \frac{-64}{-16}$

Since we do have a common ratio of 4, then we know it is a geometric sequence. Substituting everything in, we get:

$S_6 = \frac{-4(4^{6} - 1)}{4 - 1}$
$S_6 = \frac{-4(4096 - 1)}{3}$
$S_6 = \frac{-4(4095)}{3}$

By calculator, we get:
S_6 = -5460

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Ответ:

briannasineiro7937

16.10.2022

Mathematics

Can you post a picture of the problem?

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What is the sum of the first 6 terms of this geometric sequence? –4, –16, –64, –256, …a.–1024b.–4096c.–5460d.–5476?

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