Find the value of $n$ so that $\large\frac{a^{n+1}+b^{n+1}}{a^n+b^n}$ may be the geometric mean between $a$ and $b$.

Question

$\begin{array}{1 1} \large\frac{1}{2} \\ \large\frac{-1}{2} \\ 1\\ -1\end{array} $