2007 iTest Problems/Problem 29

Problem

Let $S$ be equal to the sum $1+2+3+\cdots+2007$ . Find the remainder when $S$ is divided by $1000$ .

Solution

The list of numbers is an arithmetic sequence with $2007$ terms, first term $1$ , and last term $2007$ . Using the arithmetic series sum formula, $S = \frac{2007(1+2007)}{2} = 2015028$ . The remainder when $S$ is divided by $1000$ is $\boxed{28}$ .

2007 iTest (Problems, Answer Key)
Preceded by: Problem 28	Followed by: Problem 30
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2007 iTest Problems/Problem 29

Problem

Solution

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