If $(m+n)^{th}$, $(n+1)^{th}$, $(r+1)^{th}$ term of an AP are in GP and $m, n, r$ are in HP, then ratio of first term of AP to common difference is

Question

$(a)\;n\qquad(b)\;\large\frac{n}{2}\qquad(c)\;\large\frac{n}{3}\qquad(d)\;\large\frac{-n}{2}$