#### Answer

$\displaystyle\sum_{j=1}^{10} (2j+3)=140$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To evaluate the given expression, $
\displaystyle\sum_{j=1}^{10} (2j+3)
,$ use the formula for finding the sum of $n$ terms that form an arithmetic sequence.
$\bf{\text{Solution Details:}}$
Substituting $j$ with $
1
,$ then the first term, $a_1,$ is
\begin{array}{l}\require{cancel}
a_1=2(1)+3
\\\\
a_1=2+3
\\\\
a_1=5
.\end{array}
Substituting $j$ with $
10
,$ then the last term, $a_n,$ is
\begin{array}{l}\require{cancel}
a_n=2(10)+3
\\\\
a_n=20+3
\\\\
a_n=23
.\end{array}
With $j$ going from $
1
$ to $
10
,$ then there are a total of $
10
$ terms in the series. Hence, $n=
10
.$
Using the formula for finding the sum of $n$ terms that form an arithmetic sequence, which is given by $S_n=\dfrac{n}{2}(a_1+a_n),$ then
\begin{array}{l}\require{cancel}
S_{10}=\dfrac{10}{2}(5+23)
\\\\
S_{10}=5(28)
\\\\
S_{10}=140
.\end{array}
Hence, $
\displaystyle\sum_{j=1}^{10} (2j+3)=140
.$