2016 AMC 8 Problems/Problem 19
Contents
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 2
Let be the largest number. Then, . Factoring this gives . Grouping like terms gives , and continuing down the line, we find .
~MrThinker
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 (CREATIVE THINKING + ANALYSIS!!!)
~Education, the Study of Everything
Video Solution
~savannahsolver
See Also
2016 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 18 |
Followed by Problem 20 | |
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