# An algebra problem by Alf-archie Sangkula

Algebra Level pending

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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