  Celebrated theorems of Roth and of Matou\v{s}ek and Spencer together show
that the discrepancy of arithmetic progressions in the first $n$ positive
integers is $\Theta(n^{1/4})$. We study the analogous problem in the
$\mathbb{Z}_n$ setting. We asymptotically determine the logarithm of the
discrepancy of arithmetic progressions in $\mathbb{Z}_n$ for all positive
integer $n$. We further determine up to a constant factor the discrepancy of
arithmetic progressions in $\mathbb{Z}_n$ for many $n$. For example, if $n=p^k$
is a prime power, then the discrepancy of arithmetic progressions in
$\mathbb{Z}_n$ is $\Theta(n^{1/3+r_k/(6k)})$, where $r_k \in \{0,1,2\}$ is the
remainder when $k$ is divided by $3$. This solves a problem of Hebbinghaus and
Srivastav.
