Let $t_n$ be a sequence that satisfies a first order homogeneous recurrence $t_n = Q(n)t_{n-1}$, where $Q(n) \in \mathbb{Z}[n]$. These type of sequences arise in different types of problems like the integration of rational functions and the evaluation of infinite sums. In this talk, the asymptotic behavior of the $p$-adic valuation of $t_n$ will be described.