## 2014 Singapore MO (Open Rd 1) Problem 21

2014 SMO (Open-Rd1) 21. Let $a_1, a_2, a_3, \dots, a_{2001}, \dots$ be an arithmetic progression such that $a_1^2 + a_{1001}^2 \leq 10$. Find the largest possible value of the following expression:

$a_{1001} + a_{1002} + a_{1003} + \dots + a_{2001}.$