You could simply write
"Let $r_n = 2n$ for all integers $n$ from $0$ to $7$."
or perhaps
"Let $r_n = 2n$ for $n \in \{0,1,2,\dotsc,7\}$."
or, using the compact notation suggested by Ilya,
"Let $r_n = 2n$ for $n \in \overline{0,7}$."
or even, if it's clear from context that $n$ is an integer,
"Let $r_n = 2n$ for $0 \le n \le 7$."
However, if going with Ilya's notation, be aware that many English-speaking readers may not be familiar with it, so you should define it yourself, e.g. "Let $\overline{n,m} = \{n,\,\dotsc,\,m\}$ denote the set of integers between $n$ and $m$ inclusive."
(Ps. What's wrong with MathJax's rendering of \overline
, anyway? The lines in my examples above seem to curve upwards at the ends like this, while the first — but not the second — one in Ilya's comment curves the other way.)