Finiteness for etale cohomology

Question

The groups $H_{et}(X, \mathbb{Z}/n)$ are known to be finite for smooth projective variety over the algebraic closure of $\mathbb{F}_p$. Are there finiteness/finite generation result for the etale cohomology of $\mathbb{G}_m$ and $\mu_n$ sheaves? ($n$ prime to characteristics)