KöMaL 2015 A652

Prove that there exists a real number $C>1$ with the following property: whenever $n>1$ and $a_0<a_1<\cdots<a_n$ are positive integers such that $\frac1{a_0},\frac1{a_1},\ldots,\frac1{a_n}$ form an arithmetic progression, then $a_0> C^n$.