Answer:
The sequence is geometric
The recursive formula for the sequence is:
[tex]A_n=\cdot A_{n-1}\cdot -3, A_1=-2[/tex]
The explicit formula for the sequence is
[tex]A_n= - 2 {( - 3)}^{n - 1} [/tex]
Explanation:
The given sequence is -2, 6, -18,54
There is a common ratio of
[tex]r = \frac{6}{ - 2} = \frac{ - 18}{6} = \frac{54}{ - 18} = - 3[/tex]
Since there is a common ratio, the sequence is geometric.
The first term of this sequence is
[tex]A_1=-2[/tex]
The recursive definition is given by:
[tex]A_n=r\cdot A_{n-1}[/tex]
We substitute r=-3 to get,
[tex]A_n= - 3\cdot A_{n-1}[/tex]
The explicit formula is
[tex]A_n= - 2 {( - 3)}^{n - 1} [/tex]
