Answer
The sequence is arithmetic and the sum of the first $10$ terms is $310$.
Work Step by Step
The terms have a common difference of $6$ so the sequence is arithmetic with $d=6$ and $a_1=4$.
The sum $S_n$ of the first $n$ terms of an arithmetic sequence is given by the formula:
$$S_n=\frac{n}{2}(a_1+a_n)$$
The given sequence has $a_1=4$ and $d=6$.
However, the value of $a_{10}$ is not yet known.
Solve for $a_{10}$ using the formula $a_n=a_1+(n-1)(d)$ to obtain:
\begin{align*}
a_{10}=4+(10-1)(6)\\
&=4+9(6)\\
&=4+54\\
&=58
\end{align*}
Use the formula for the sum of the first $n$ terms to obtain the sum of the first $10$ terms (use $n=10$) to obtain:
\begin{align*}
S_{10}=\frac{10}{2}(4+58)\\
&=5(62)\\
&=310
\end{align*}
