Explanation

(c)
Since, $\frac{a + b}{2} = \frac{a^{n} + b^{n}}{a^{n - 1} + b^{n - 1}}$
$\Rightarrow (a + b)\left( a^{n - 1} + b^{n - 1} \right) = 2(a^{n} + b^{n})$
$\Rightarrow \frac{ab^{n}}{b} + \frac{ba^{n}}{a} = a^{n} + b^{n}$
$\Rightarrow \ a^{n}\left( \frac{a - b}{a} \right) = - b^{n}\left( \frac{b - a}{b} \right)$
$\Rightarrow \ \frac{a^{n}}{b^{n}} = \frac{a}{b}\ \Rightarrow n = 1$