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