Question

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

Answer 1

$a_1=4;\ a_2=-12\\\\r=\dfrac{a_2}{a_1}\to r=\dfrac{-12}{4}=-3$

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