Question

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

Answer 1

The common ratio in a geometric sequence is the ratio between 2 consecutive terms:

-8/2=-4, 

then the sequence is  2, -8, 32, -128, -512, 2048, ...

let $a_n$ be the nth term of the sequence, then 

$a_1= 2$
$a_2=2(-4)$
$a_3=2(-4)(-4)=2(-4)^{2}$
$a_4=2(-4)(-4)(-4)=2(-4)^{3}$
.
.
.
so clearly $a_n=2(-4)^{n-1}$

and, clearly n are integers >0, since we have a 1st term, a second term and so on... of a sequence (we do not have a "zero'th term"!

Answer:

C. an=2(-4)^n-1; all integers where n>0