Answer
$a_n=5n-4$
Work Step by Step
Let's note the arithmetic sequence by $\{a_n\}$ and the common difference by $d$. We are given:
$$\begin{cases}
a_{20}=96\\
d=5.
\end{cases}$$
The formula of the $n$th term is:
$$a_n=a_1+(n-1)d.\tag1$$
We are given $d$, so we determine $a_1$ using $a_{20}$ and $d$:
$$\begin{align*}
a_{20}&=a_1+19d\\
a_1&=a_{20}-19d\\
&=96-19(5)\\
&=1.
\end{align*}$$
Our sequence is:
$$\begin{cases}
a_1=1\\
d=5.
\end{cases}$$
We determine the $n$th element:
$$a_n=1+(n-1)(5)=1+5n-5=5n-4.$$
So the $n$th term is $5n-4$.
