Question

!!!!!!!! 50 POINTS !!!!!!!!What are the explicit equation and domain for a geometric sequence with a first term of 2 and a second term of −8?

an = 2(−8)^(n − 1); all integers where n ≥ 1
an = 2(−8)^(n − 1); all integers where n ≥ 0
an = 2(−4)^(n − 1); all integers where n ≥ 0
an = 2(−4)^(n − 1); all integers where n ≥ 1

Answer 1

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

Explanation:

The equation has the form ...

an = a1(r)^(n-1) . . . . . where a1 is the first term and r is the common ratio.

The first term is given as 2, and the ratio will be the ratio of the first two terms:

r = (-8)/(2) = -4

Terms are numbered starting with n=1, so the formula is ...

an = 2(-4)^(n-1) for n≥1