Difference between revisions of "2016 AMC 8 Problems/Problem 19"
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==Video Solution== | ==Video Solution== |
Revision as of 22:10, 17 May 2024
Problem
The sum of consecutive even integers is . What is the largest of these consecutive integers?
Solution 1
Let be the 13th consecutive even integer that's being added up. By doing this, we can see that the sum of all 25 even numbers will simplify to since . Now, . Remembering that this is the 13th integer, we wish to find the 25th, which is .
Solution 3
Let be the smallest number. The equation will become, . After you combine like terms, you get which turns into . , so . Then, you add .
~AfterglowBlaziken
Video Solution
~savannahsolver
See Also
2016 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 18 |
Followed by Problem 20 | |
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 | ||
All AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.