Question

find the sum of the first 13 terms of the geometric sequence. use the formula for the su
4, -12, 36, -108, ...

the sum of the first 13 terms of the geometric sequence is
(simplify your answer.)

Explanation:

Step1: Identify \(a_1\), \(r\), \(n\)

For the geometric sequence \(4, -12, 36, -108, \dots\), the first term \(a_1 = 4\). The common ratio \(r=\frac{-12}{4}=-3\). We need the sum of the first \(n = 13\) terms.

Step2: Use the sum formula for geometric series

The formula for the sum of the first \(n\) terms of a geometric series is \(S_n=\frac{a_1(1 - r^n)}{1 - r}\) (when \(r
eq1\)).
Substitute \(a_1 = 4\), \(r=-3\), and \(n = 13\) into the formula:

$$
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Answer:

\(1594324\)