# AIME 2015 Problem 13

Algebra Level 5

Define the sequence $$a_1, a_2, a_3, \ldots$$ by $$a_n = \sum\limits_{k=1}^n \sin{k}$$, where $$k$$ represents radian measure. Find the index of the $$100$$th term for which $$a_n < 0$$.

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