Answer
$a_n=9n-70$
Work Step by Step
Let $a_n$ be our arithmetic sequence. We are given:
$$\begin{align*}
a_6&=-16\\
d&=9.
\end{align*}$$
We determine the first term $a_1$:
$$\begin{align*}
a_n&=a_1+(n-1)d\\
a_6&=a_1+(6-1)d\\
-16&=a_1+5(9)\\
-16-45&=a_1\\
a_1&=-61.
\end{align*}$$
We write the rule for the general term $a_n$:
$$\begin{align*}
a_n&=a_1+(n-1)d\\
a_n&=-61+(n-1)(9)=-61+9n-9=9n-70.
\end{align*}$$
We got:
$$a_n=9n-70.\tag1$$
We calculate the first six terms substituting $n=2,3,4,5$ in Eq. $(1)$ and $a_1=-61$, $a_6=-16$:
$$\begin{align*}
a_1&=-61\\
a_2&=9(2)-70=-52\\
a_3&=9(3)-70=-43\\
a_4&=9(4)-70=-34\\
a_5&=9(5)-70=-25\\
a_6&=-16.
\end{align*}$$
Graph the first six terms:
