Answer
$a_{n}=9-3n$
Work Step by Step
We will use the equation for an arithmetic sequence$:$
$$a_{n}=a_{1}+(n-1)d$$
The first term is $a_{1}=6$, and the common difference between the terms is
$$d=3-6=-3.$$
Substitute $6$ for $a_{1}$, and $-3$ for $d$, and simplify:
$$\begin{align*}
a_{n}&=6+(n-1)(-3)& & \\
&=6-3n+3 \\
&=9-3n \end{align*}$$
