Can We Apply AM-GM?

Calculus Level 4

$\large \displaystyle \lim_{n \to \infty} \dfrac {A_n}{G_n}$

Let $a_1, a_2, \ldots, a_n$ be an arithmetic progression composed solely of distinct positive reals.

Also, let $A_n$ denote its arithmetic mean and $G_n$ denote its geometric mean.

What is the value of the above limit to 3 decimal places?

If you think the limit doesn't exist, write -13.37 as your answer.