Answer
$a_n=3.5n-5$
Work Step by Step
Let $a_n$ be our arithmetic sequence. We are given:
$$\begin{align*}
a_{10}&=30\\
d&=3.5.
\end{align*}$$
We determine the first term $a_1$:
$$\begin{align*}
a_n&=a_1+(n-1)d\\
a_{10}&=a_1+(10-1)d\\
30&=a_1+9(3.5)\\
30-31.5&=a_1\\
a_1&=-1.5.
\end{align*}$$
We write the rule for the general term $a_n$:
$$\begin{align*}
a_n&=a_1+(n-1)d\\
a_n&=-1.5+(n-1)(3.5)\\
&=-1.5+3.5n-3.5\\
&=3.5n-5.
\end{align*}$$
We got:
$$a_n=3.5n-5.\tag1$$
We calculate the first six terms substituting $n=2,3,4,5,6$ in Eq. $(1)$ and $a_1=-1.5$:
$$\begin{align*}
a_1&=-1.5\\
a_2&=3.5(2)-5=2\\
a_3&=3.5(3)-5=5.5\\
a_4&=3.5(4)-5=9\\
a_5&=3.5(5)-5=12.5\\
a_6&=3.5(6)-5=16.
\end{align*}$$
Graph the first six terms:
