ANSWER
[tex]a_n=4( { (- 2)}^{n - 1} )[/tex]
for n≥1
EXPLANATION
The explicit equation for a geometric sequence is found using the formula:
[tex]a_n=a_1( {r}^{n - 1} )[/tex]
where
[tex]a_1 = 4[/tex]
is the first term and
[tex]r =\frac{- 8}{4}=-2[/tex]
is the common ratio.
We substitute the values into the formula to obtain,
[tex]a_n=4( { (- 2)}^{n - 1} )[/tex]
This is the explicit formula for the geometric sequence.
The domain is n≥1
