Question

$\frac{a^n+b^n}{a^{n-1}+b^{n-1}}$ is the AM between $a$ and $b$ if $n$ is

• A. $0$
• B. $\frac{1}{2}$
• C. $1$
• D. $-1$

Answer 1

The correct option is C $1$

$AM$ between $a$ and $b$ is $\frac{(a+b)}{2}$

$AM=\frac{a^n+b^n}{a^{n-1}+b^{n-1}}=\frac{a+b}{2}=\frac{a+b}{1+1}=\frac{a^{\prime }+b^{\prime }}{a^{\circ }+b^{\circ }}$

$\Rightarrow n=1$