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}.

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