If $\frac{a^{n+1}+b^{n+1}}{a^n+b^n}$ is the G.M between $a$ and b then $\mathrm{n}=$

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Professor PC Thomas Classes · Answer

The general form for the mean is $\frac{a^{n+1}+b^{n+1}}{a^n+b^n}$. For Geometric Mean (G.M.), this expression equals $\sqrt{ab} = a^{1/2}b^{1/2}$. Comparing the exponents, we find that $n = -1/2$ for G.M.