Answer
$a_{n}=29-7n$
Work Step by Step
We will use the equation for an arithmetic sequence$:$
$$a_{n}=a_{1}+(n-1)d$$
The first term is $a_{1}=22$, and the common difference between the terms is
$$d=15-22=-7.$$
Substitute $22$ for $a_{1}$, and $-7$ for $d$, and simplify:
$$\begin{align*}
a_{n}&=22+(n-1)(-7)& & \\
&=22-7n+7 \\
&=29-7n \end{align*}$$
