Answer
$S_{10}=230$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To find $S_{10}$ in the given sequence
\begin{array}{l}\require{cancel}
5,9,13,...
\end{array}
use the formula for finding the sum of the first $n$ terms of an arithmetic sequence.
$\bf{\text{Solution Details:}}$
The common difference, $d,$ of an arithmetic sequence is the difference of a term and the term preceeding it. Hence, the common difference of the given sequence is
\begin{array}{l}\require{cancel}
d=a_2-a_1
\\\\
d=9-5
\\\\
d=4
.\end{array}
Using the formula for the sum of the first $n$ terms of an airthmetic sequence, which is given by $
S_n=\dfrac{n}{2}[2a_1+(n-1)d]
,$ then the sum of the first $n=10$ terms with $a_1=5$ and $d=4$ is
\begin{array}{l}\require{cancel}
S_n=\dfrac{n}{2}[2a_1+(n-1)d]
\\\\
S_{10}=\dfrac{10}{2}[2\cdot5+(10-1)4]
\\\\
S_{10}=5[10+(9)4]
\\\\
S_{10}=5[10+36]
\\\\
S_{10}=5[46]
\\\\
S_{10}=230
.\end{array}
