Answer:
[tex]a_n=-3 \cdot a_{n-1}[/tex]
[tex]a_1=2[/tex]
You gave the explicit form.
Step-by-step explanation:
You gave the explicit form.
The recursive form is giving you a term in terms of previous terms of the sequence.
So the recursive form of a geometric sequence is [tex]a_n=r \cdot a_{n-1}[/tex] and they also give a term of the sequence; like first term is such and such number. All this says is to get a term in the sequence you just multiply previous term by the common ratio.
r is the common ratio and can found by choosing a term and dividing by the term that is right before it.
So here r=-3 since all of these say that it does:
-54/18
18/-6
-6/2
If these quotients didn't match, then it wouldn't be geometric.
Anyways the recursive form for this geometric sequence is
[tex]a_n=-3 \cdot a_{n-1}[/tex]
[tex]a_1=2[/tex]
