1. Let the arithmetic sequence $\left\{a_{n}\right\}$ satisfy $3 a_{8}=5 a_{13}$, and $a_{1}>0, S_{n}$ be the sum of the first $n$ terms, $S_{n}\left(n \in \mathbf{N}_{+}\right)$ has the maximum value at $\qquad$ .
1. $S_{20}$.

Let $a_{n}=a_{1}+(n-1) d$, then $3\left(a_{1}+7 d\right)=5\left(a_{1}+12 d\right)$, so $a_{1}=-\frac{39}{2} d>0$, and $d<0, a_{21}<0$. Therefore, $S_{20}$ is the maximum.