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 $S_{n}(n \in \mathrm{N})$ 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 $3\left(a_{1}+7 d\right)=$ $5\left(a_{1}+12 d\right)$. That is, $a_{1}=-19.5 d$, thus we know $a_{20}=a_{1}+19 d>0$ and $a_{21}=a_{1}+20 d<0$,
$\therefore$ the sum of the first 20 terms of the arithmetic sequence is the maximum, hence the answer is (C).