Question 24
Let $\{a_1,a_2,a_3,\ldots\}$ be a sequence of real numbers. Let $\{b_1,b_2,b_3,\ldots\}$ be a sequence of real numbers such that $b_n=a_{n+1}-a_n$ for all $n\ge1$. Determine the maximum value of $a_n$ within the sequence $\{a_1,a_2,a_3,\ldots\}$ if $b_{m+1}-b_m=-2$ for all $m\ge1$, $a_5=615$ and $a_{10}=1045$.