Question

Can someone help idk if this is right

Answer 1

`a_n=-3 \cdot a_(n-1)`

`a_1=2`

You gave the explicit form.

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
`a_n=r \cdot a_(n-1)` 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

`a_n=-3 \cdot a_(n-1)`

`a_1=2`