If $n$ is odd, then in how many ways $3$ numbers that are in A.P. can be selected from the numbers $1,2,3,...............n$?

Question

$\begin{array}{1 1} (A) \large\frac{(n+1)^2}{4} \\ (B) \large\frac{(n-1)^2}{2} \\ (C) \large\frac{(n-1)^2}{4} \\ (D) \large\frac{(n+1)^2}{2} \end{array} $