Represent the geometric series using the explicit formula.

12, −36, 108, −324, …

f(n) = f(n − 1) ⋅ (−3)
f(n) = f(n − 1) ⋅ (3)
f(n) = 12 ⋅ (−3)(n−1)
f(n) = 12 ⋅ (3)(n−1)

answer:

 f(n)=12(-3)^{(n-1)}

Step-by-step explanation:

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

Where  is the nth term of the sequence,  is the first term in the sequence and  is the common ratio.

Given the following geometric serie:

The common ratio is:

And the first term is:

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