Answer: [tex]a_n=4(-3)^{n-1}[/tex]
Domain: Set of Natural numbers.
Step-by-step explanation:
The general explicit equation for the nth term of a geometric sequence is:
[tex]a_n=a_{1}r^{n-1}[/tex], where r is the common ratio.
Given: First term =[tex]a_1=4[/tex]
Second term =[tex]a_2=-12[/tex]
Common Ratio=[tex]r=\dfrac{a_2}{a_1}=\dfrac{-12}{4}=-3[/tex]
Now, the explicit equation for given geometric sequence is:
[tex]a_n=4(-3)^{n-1}[/tex]
- The domain of the geometric sequence is always the set of natural numbers , since each term has an order which can only represent by natural number.
