Answer:
1. Geometric sequence
2. [tex]-2(-3)^{n-1}[/tex] ; [tex]A_{1}=-2[/tex]
3. [tex]A_{n}=-2(-3)^{n-1}[/tex]
Step-by-step explanation:
The sequence is Geometric.
For the sequence to be Geometric , then there must exist a common ratio
check:
6/-2 = -18/6 = 54/-18 = -3
The recursive formula for the sequence is :
[tex]-2(-3)^{n-1}[/tex] ; [tex]A_{1}=-2[/tex]
To find the explicit formula:
The formula for the nth term of a Geometric sequence is given as :
[tex]A_{n}=ar^{n-1}[/tex]
where :
a = first term
r = common ratio
so , substituting the values into the formula , we have :
[tex]A_{n}=-2(-3)^{n-1}[/tex]
therefore : the explicit formula = [tex]A_{n}=-2(-3)^{n-1}[/tex]
