Farey sequences

A fraction $h/k$ is called a proper fraction if it lies between $0$ and $1$, and $h$ and $k$ have no common divisors other than $1$. For any natural number n \geq 1, the Farey sequence of order $n$, denoted as $\text{F}[n]$, is the sequence of all proper fractions with denominators not exceeding $n$, together with the "fraction" $1/1$, arranged in increasing order. For example, the sequence $\text{F}[5]$ is:

Given $n$, find the $k$-th fraction in the sequence $\text{F}[n]$.