so they start off with 5 bricks, then they add 2 bricks on the left side and 2 bricks on the right side, namely 4 bricks, so the first row is 5 bricks, the next row is 5+4 or 9 bricks and so on.
5, 9, 13, 17.... <--- as you can see the "common difference" is 4.
[tex]\bf n^{th}\textit{ term of an arithmetic sequence}
\\\\
a_n=a_1+(n-1)d\qquad
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
d=\textit{common difference}\\
----------\\
a_1=5\\
d=4\\
n=25
\end{cases}
\\\\\\
a_{25}=5+(25-1)(4)\implies a_{25}=5+(24)(4)
\\\\\\
a_{25}=5+96\implies a_{25}=101\\\\
-------------------------------[/tex]
[tex]\bf \textit{ sum of a finite arithmetic sequence}
\\\\
S_n=\cfrac{n(a_1+a_n)}{2}\qquad
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
----------\\
a_1=5\\
a_{25}=101\\
n=25
\end{cases}
\\\\\\
S_{25}=\cfrac{25(5+101)}{2}\implies S_{25}=\cfrac{25(106)}{2}\implies S_{25}=1325[/tex]
