Answer: [tex]f(n)=12(-3)^{(n-1)}[/tex]
Step-by-step explanation:
The Explicit formula in function notation for a geometric series is:
[tex]f(n)=f(1)r^{(n-1)}[/tex]
Where [tex]f(n)[/tex] is the nth term of the sequence, [tex]f(1)[/tex] is the first term in the sequence and [tex]r[/tex] is the common ratio.
Given the following geometric serie:
[tex]12, -36, 108, -324...[/tex]
The common ratio is:
[tex]r=\frac{-36}{12}=-3[/tex]
And the first term is:
[tex]f(1)=12[/tex]
Therefore, substituting values, we get that the Explicit formula that represents this geometric series is:
[tex]f(n)=12(-3)^{(n-1)}[/tex]
