Question 69
For each positive integer $n$ let the set $A_{n}$ consist of all numbers $\pm 1 \pm 2 \pm \ldots \pm n$. For example,
$$
\begin{gathered}
A_{1}=\{-1,1\}, \quad A_{2}=\{-3,-1,1,3\} \\
A_{3}=\{-6,-4,-2,0,2,4,6\}
\end{gathered}
$$
Find the number of elements in $A_{n}$.
$$
\begin{gathered}
A_{1}=\{-1,1\}, \quad A_{2}=\{-3,-1,1,3\} \\
A_{3}=\{-6,-4,-2,0,2,4,6\}
\end{gathered}
$$
Find the number of elements in $A_{n}$.