College Algebra, Chapter 9, 9.2, Section 9.2, Problem 62

Suppose telephone poles are stored in a pile with 25 poles in the first layer, 24 in the second, and so on. If there are 12 layers, how many telephone poles does the pile contain?

If $a_1 = 25$ and $a_2 = 24$, then their common difference $d = -1$. And if $n = 12$, then the total poles will be


$
\begin{equation}
\begin{aligned}

S_n =& \frac{n}{2} [2a + (n-1) d]
\\
\\
S_{12} =& \frac{12}{2} [2(25) + (12-1)(-1)]
\\
\\
S_{12} =& 6 [50 + 11(-1)]
\\
\\
S_{12} =& 6 [50-11]
\\
\\
S_{12} =& 6(39)
\\
\\
S_{12} =& 234

\end{aligned}
\end{equation}
$


It means that there are total of $234$ number of poles stored in a pile.