Question

Consider the sequence -2, 6, -18,54 Select all of the statements that are true for the sequence.

Answer 1

Answer:

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

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

Explanation:

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

There is a common ratio of

$r = \frac{6}{ - 2} = \frac{ - 18}{6} = \frac{54}{ - 18} = - 3$

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

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