Question

Consider the sequence -2, 6, -18,54

Select all of the statements that are true for the sequence.

Answer 1

The sequence is geometric

The recursive formula for the sequence is:

`A_n=\cdot A_(n-1)\cdot -3, A_1=-2`

The explicit formula for the sequence is

`A_n= - 2 {( - 3)}^(n - 1)`

Step-by-step explanation:

The given sequence is -2, 6, -18,54

There is a common ratio of

`r = (6)/( - 2) = ( - 18)/(6) = (54)/( - 18) = - 3`

Since there is a common ratio, the sequence is geometric.

The first term of this sequence is

`A_1=-2`

The recursive definition is given by:

`A_n=r\cdot A_(n-1)`

We substitute r=-3 to get,

`A_n= - 3\cdot A_(n-1)`

The explicit formula is

`A_n= - 2 {( - 3)}^(n - 1)`