Given that $a\;\xi\;b$ are not equal , find the value of n so that $\frac{a^{n+1}+b^{n+1}}{a^n+b^n}$ is the GM of $a\;\xi\;b$

Question

$(a)\;n=\frac{-1}{3}\qquad(b)\;n=3\qquad(c)\;n=2\qquad(d)\;n=\frac{-1}{2}$