Question

20 points algebra question

Answer 1

1. Geometric sequence

2.
`-2(-3)^(n-1)` ;
`A_(1)=-2`

3.
`A_(n)=-2(-3)^(n-1)`

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 :

`-2(-3)^(n-1)` ;
`A_(1)=-2`

To find the explicit formula:

The formula for the nth term of a Geometric sequence is given as :

`A_(n)=ar^(n-1)`

where :

a = first term

r = common ratio

so , substituting the values into the formula , we have :

`A_(n)=-2(-3)^(n-1)`

therefore : the explicit formula =
`A_(n)=-2(-3)^(n-1)`