Question

What are the explicit equation and domain for a geometric sequence with a first term of 4 and a second term of −12?

A. an = 4(−3)n − 1; all integers where n ≥ 1

B. an = 4(−3)n − 1; all integers where n ≥ 0

C. an = 4(36)n − 1; all integers where n ≥ 1

D. an = 4(36)n − 1; all integers where n ≥ 0

Answer 1

`a_1=4;\ a_2=-12\\\\r=(a_2)/(a_1)\to r=(-12)/(4)=-3`

The formula of a geometric sequence:


`a_n=a_1\cdot r^(n-1)`

substitute


`a_n=4\cdot(-3)^(n-1)`


`The\ domain:\ \text{all integers where}\ n\geq1`

Answer:
`\boxed{a_n=4(-3)^(n-1);\ \text{all integers where}\ n\geq1}`