Question

Represent the geometric series using the explicit formula.

Answer 1

Answer:  $f(n)=12(-3)^{(n-1)}$

Step-by-step explanation:

The Explicit formula in function notation for a geometric series is:

$f(n)=f(1)r^{(n-1)}$

Where $f(n)$ is the nth term of the sequence, $f(1)$ is the first term in the sequence and $r$ is the common ratio.

Given the following geometric serie:

$12, -36, 108, -324...$

The common ratio is:

$r=\frac{-36}{12}=-3$

And the first term is:

$f(1)=12$

Therefore, substituting values, we get that the Explicit formula that represents this geometric series is:

$f(n)=12(-3)^{(n-1)}$