Question 4Suppose that $a_1,a_2,a_3,a_4,\ldots$ is an arithmetic progression with $a_1>0$ and $3a_8=5a_{13}$. Let $S_n=a_1+a_2+\cdots+a_n$ for all integers $n\ge1$. Find the integer $n$ such that $S_n$ has the maximum value.