If $\;\bigtriangleup_{r}=\begin{vmatrix} r & 2r-1 & 3r-2 \\[0.3em] \large\frac{n}{2} & n-1 & a \\[0.3em] \large\frac{1}{2}n(n-\normalsize 1) & (n-\normalsize 1)^{2} & \large\frac{1}{2} (n-\normalsize 1)(\normalsize 3n-\normalsize 4)\end{vmatrix}\;$ , then the value of $\;\sum_{r=1}^{n-1} \bigtriangleup_{r}\;$ :

Question

(a) depends only on a (b) depends only on n (c) depends both on a and n (d) is independent of both a and n