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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