$a_{1}=50$ and $a_{1}+a_{2}+....+a_{n}=n^2a_{n}$ $\forall\;n \geq 1$, value of $a_{50}$ equal to

Question

$(a)\;\large\frac{1}{51}\qquad(b)\;\large\frac{2}{51}\qquad(c)\;\large\frac{1}{101}\qquad(d)\;\large\frac{2}{101}$