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 its first $n$ terms. Then the largest $S_{n}(n \in N)$ is ( ).
(A) $S_{10}$
(B) $S_{11}$
(C) $S_{20}$
(D) $S_{21}$
$-1 .(C)$
Let the common difference of the arithmetic sequence be $d$. Then, from $3 a_{8}=5 a_{13}$, we get $3\left(a_{1}+7 d\right)=5\left(a_{1}+12 d\right)$, which simplifies to $a_{1}=-19.5d$. Therefore, $a_{20}$ $=a_{1}+19 d>0$, and $a_{21}=a_{1}+20 d<0$. Hence, the sum of the first 20 terms of this arithmetic sequence is the maximum.