Define the sequence <img alt="$a_1, a_2, a_3, \ldots$" height="11" src="https://latex.artofproblemsolving.com/c/4/a/c4a82e7c7dbf7b035a66b5890ec80463b4c3e8d9.png" width="95" /> by <img alt="$a_n = \sum\limits_{k=1}^n \sin{k}$" height="48" src="https://latex.artofproblemsolving.com/7/b/0/7b0b99322612a80b3f24176bc81dfffa51642e45.png" width="106" />, where <img alt="$k$" height="12" src="https://latex.artofproblemsolving.com/8/c/3/8c325612684d41304b9751c175df7bcc0f61f64f.png" width="9" /> represents radian measure. Find the index of the 100th term for which <img alt="$a_n < 0$" height="15" src="https://latex.artofproblemsolving.com/b/2/e/b2e64135fcfc3b060e2dff4ffd1ba37ad2757f98.png" width="51" />.   **Trigonometry**

Question No: 392

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 100th term for which $a_n < 0$ .

**Trigonometry**

Editorial

Tags: Algebra

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