Difference between revisions of "2007 iTest Problems/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]] | ||
Latest 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 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 • 51 • 52 • 53 • 54 • 55 • 56 • 57 • 58 • 59 • 60 • TB1 • TB2 • TB3 • TB4 | ||
