1. (1995 National High School League Question) 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 its first $n$ terms, then the largest $S_{n}\left(n \in \mathbf{N}_{+}\right)$ is ( ).
A. $S_{10}$
B. $S_{11}$
C. $S_{20}$
D. $S_{21}$
1. C. Let the common difference be $d$, then $3\left(a_{1}+7 d\right)=5\left(a_{1}+12 d\right)$, so $a_{1}=-\frac{39}{2} d>0$, thus $d<0$, $a_{21}=a_{1}+20 d=\frac{1}{2} d<0$, hence $S_{20}$ is the maximum, so the answer is C.