Answer
$a_n=6n-1$
$a_{20}=119$
Work Step by Step
Let $a_n$ be our sequence. We are given:
$$\begin{align*}
a_1&=5\\
a_2&=11\\
a_3&=17\\
a_4&=23\\
a_5&=29.
\end{align*}$$
We notice that we have:
$$a_2-a_1=a_3-a_2=a_4-a_3=a_5-a_4=6.$$
This means that the sequence is arithmetic. Its first term $a_1$ and common difference $d$ are:
$$\begin{align*}
a_1&=5\\
d&=6.
\end{align*}$$
We write the rule for the general term $a_n$:
$$\begin{align*}
a_n&=a_1+(n-1)d\\
a_n&=5+(n-1)(6)=5+6n-6=6n-1.
\end{align*}$$
We got:
$$a_n=6n-1.\tag1$$
We calculate $a_{20}$ substituting $n=20$ in Eq. $(1)$:
$$a_{20}=6(20)-1=119.$$
