SEAMO 2027 - Paper F - SET 03 - Self-study Question 25

An arithmetic progression $a_1,a_2,a_3,\ldots$ satisfies $a_1>0$ and $3a_8=5a_{13}$. Let $S_n=a_1+a_2+\cdots+a_n$ for integers $n\ge1$. Find the integer $n$ for which $S_n$ is greatest.