The Solution:
Given:
[tex]a_n=a_{n-1}.-6[/tex]
Required:
To find the recursive formula for the sequence.
The recursive formula for a geometric sequence is:
[tex]a_n=a_1.r^{n-1}[/tex]
From the given formula, we can find r as below:
[tex]\begin{gathered} a_n=a_{n-1}.-6 \\ \\ a_n=(-6)a_{n-1} \\ \\ \text{ Divide both sides by }a_{n-1} \\ \\ -6=\frac{a_n}{a_{n-1}}=r \\ \\ r=-6 \end{gathered}[/tex]
Recall:
[tex]a_1=-4\text{ \lparen given\rparen}[/tex]
So, the explicit form of the recursive formula is:
[tex]a_n=(-4)(-6)^^{n-1}[/tex]
