The sum of 5 consecutive integers is 10n + 5. What is the median of the 5 integers in terms of n?
How can you prove that it must be 2n + 1?
Call the first of the consecutive integers "i". Then the next four integers are i+1, i+2, i+3, and i+4. The sum of those five numbers is i+ (i+1)+ (i+ 3)+ (i+ 4)+ (i+ 5)= 5i+ 10= 10n+ 5. Solve that for i in terms of n. The "median" is the middle number, i+ 2.