Respuesta :

I believe the answer is;

an = 4(−2)n − 1; all integers where n ≥ 1 

Answer:

The explicit equation for the given geometric sequence is [tex]a_n=4(-2)^{n-1}[/tex]. The domain for the geometric sequence is all positive integers except 0.

Step-by-step explanation:

It is given that the first term of the geometric sequence is 4 and the second term is -8.

[tex]a_1=4,a_2=-8[/tex]

The common ratio for the sequence is

[tex]r=\frac{a_2}{a_1}=\frac{-8}{4}=-2[/tex]

The explicit equation for a given geometric sequence is

[tex]a_n=ar^{n-1}[/tex]

where, a is first term, n is number of term and r is common ratio.

The explicit equation for the given geometric sequence is

[tex]a_n=4(-2)^{n-1}[/tex]

Here n is the number of term. So, the value of n is must be a positive integer except 0.

Therefore the domain for the geometric sequence is all positive integers except 0.

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