Answer
234
Work Step by Step
The number of poles in a layer form an arithmetic sequence, with
$a=25$ and common difference $d=-1$.
The number of poles in the first 12 layers is
the sum of the first 12 terms of the arithmetic sequence,
$S_{n}=\displaystyle \frac{n}{2}[2a+(n-1)d]$
$S_{12}=\displaystyle \frac{12}{2}[2(25)+11(-1)]$
$=6\cdot 39$
$=234$
