Given a geometric sequence in the table below, create the explicit formula and list any restrictions to the domain.

nan
13
2−6
312 an = −2(3)^n − 1 where n ≥ 3

an = −3(3)^n − 1 where n ≥ 3

an = 3(−2)^n − 1 where n ≥ 1

an = 3(−3)^n − 1 where n ≥ 1

The
geometric sequence is defined as a(n+1)/an=q, q is not equal 0
so we can find easily q by a3/a2=a2/a1=12/-6= -6/3= -2
so the expresion is an=apq^n-p
where ap is the first term, for our case, ap=a1=3,so an =3(-2)^n-1
so the true answer is
an = 3(−2)^n − 1 where n ≥ 1

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