2007 iTest Problems/Problem 29: Difference between revisions
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Rockmanex3 (talk | contribs) Solution to Problem 29 |
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Let <math>S</math> be equal to the sum <math>1+2+3+\cdots+2007</math>. Find the remainder when <math>S</math> is divided by <math>1000</math>. | Let <math>S</math> be equal to the sum <math>1+2+3+\cdots+2007</math>. Find the remainder when <math>S</math> is divided by <math>1000</math>. | ||
== Solution == | ==Solution== | ||
The list of numbers is an [[arithmetic sequence]] with <math>2007</math> terms, first term <math>1</math>, and last term <math>2007</math>. Using the arithmetic series sum formula, <math>S = \frac{2007(1+2007}{2} = 2015028</math>. The remainder when <math>S</math> is divided by <math>1000</math> is <math>\boxed{28}</math>. | |||
==See Also== | |||
{{iTest box|year=2007|num-b=28|num-a=30}} | |||
[[Category:Introductory Algebra Problems]] | |||
Revision as of 18:16, 10 June 2018
Problem
Let 
be equal to the sum 
. Find the remainder when is divided by 
.
Solution
The list of numbers is an arithmetic sequence with 
terms, first term 
, and last term . Using the arithmetic series sum formula, 
. The remainder when is divided by is 
.
See Also
| 2007 iTest (Problems, Answer Key) | ||
| Preceded by: Problem 28 |
Followed by: Problem 30 | |
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