# Find the value of n such that $\frac{5^{(n+1)}+17^{(n+1)}}{5^n+17^n}$ is the AM of 5 and 17

$\begin{array}{1 1} n=1 \\ n=2 \\ n=0 \\ n=-1 \end{array}$

Answer : (c) n=0
Explanation : AM of 5 and 17 is
$\frac{5+17}{2}=\frac{22}{2}=11$
$\frac{5^{n+1}+17^{n+1}}{5^n+17^n}=11$
$5^{n+1}+17^{n+1}=11(5^n+17^n)$
$17^n (17-11) =\;5^n\;(11-5)$
$17^n\;.6=5^n\;.6$
$17^n=5^n$
$n=0.$
answered Jan 3, 2014 by