(3) In the arithmetic sequence $\left\{a_{n}\right\}$, $a_{1}>0,3 a_{8}=5 a_{13}$, then the largest partial sum $S_{n}$ is ( ).
(A) $S_{10}$
(B) $S_{11}$
(C) $S_{20}$
(D) $S_{21}$
(3) $\mathrm{C}$ Hint: From the problem, we know,
$$
3 a_{8}=5 a_{13} \Rightarrow 3\left(a_{1}+7 d\right)=5\left(a_{1}+12 d\right) \Rightarrow d=-\frac{2}{39} a_{1}0 \Rightarrow n<20.5 \text {, }
$$

From this, we can deduce that when $n=20$, $S_{n}$ is maximized.