2004 AMC 12A Problems/Problem 10
Problem
The sum of consecutive integers is . What is their median?
Solutions
Solution 1
The median of a sequence is the middle number of the sequence when the sequence is arranged in order. Since the integers are consecutive, the median is also the mean, so the median is .
Solution 2
Notice that . So, our middle number (median) must be since all the other terms can be grouped to form an additional copies . Adding them would give .
Solution by franzliszt
See also
2004 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 9 |
Followed by Problem 11 |
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 AMC 12 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.