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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

Verified Answer :

caylus

Hello,

The question is
"What are the explicit equation and domain for a geometric sequence with a first term of 2 and a second term of −8?"

It is a geometric sequence =>U(2)=U(1)r==>-8=2r ==>r=-4

U(1)=2=2(-4)^0
U(2)=-8=2(-4)=2(-4)^1
U(3)=32=-8(-4)=2(-4)(-4)=2(-4)^2
U(4)=-128=32(-4)=2(-4)^3
...
U(n)=2*(-4)^(n-1) where n>=1.

Answer C