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
~kafuu_chino
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
Solution 3
~Kathan