2024 AMC 12B Problems/Problem 11
Contents
[hide]Problem
Let . What is the mean of ?
Solution 1
Add up with , with , and with . Notice by the Pythagorean identity. Since we can pair up with and keep going until with , we get Hence the mean is
Solution 2
We can add a term into the list, and the total sum of the terms won't be affected since . Once is added into the list, the average of the terms is clearly . Hence the total sum of the terms is . To get the average of the original , we merely divide by to get . Hence the mean is
~tsun26
Notice that $x_0+x_1+\cdots+x_{90}
See also
2024 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 10 |
Followed by Problem 12 |
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 |
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