SOLUTION: Given three consecutive integers, what is the difference between the average of their squares and the square of their average?

Question 456820: Given three consecutive integers, what is the difference between the average of their squares and the square of their average?
Answer by spacesurfer(12) (Show Source): You can put this solution on YOUR website!
Did you try to do this your self? Just do the math:
If a = first integer, then a+1, and a+2 are the other consecutive integers. The average of the squares is:
=
The square of the average is:
=
Hence, the difference is 5/3 - 1 = 2/3.
If the integers didn't increase by 1 and instead increased by b, so like instead of 3,4,5, it was 3, 3+b, 3+2b, for any b (if b = 2, then 3, 5, 7), then the difference is .
if b = 1, then this reduces to 2/3, which we got earlier.
RELATED QUESTIONS
The difference between the squares of two positive integers is 376 and their positive... (answered by Edwin McCravy)

Find two consecutive positive and odd integers such that the difference of their squares... (answered by Alan3354,Gersid)

1. If the product of two consecutive odd integers is 783, what is the sum of their... (answered by stanbon,Alan3354)

Consecutive Integers. Find three consecutive integers such that the sum of their squares... (answered by checkley77)

What are three consecutive even integers if the sum of their squares is... (answered by ikleyn,greenestamps)

find two consecutive odd integers such that the difference of their squares is... (answered by rapaljer)

find two consecutive positive odd integers such that the difference of their squares is... (answered by Alan3354)

Find two consecutive odd integers such that the difference of their squares is... (answered by mananth)

the difference between the squares of two consecutive integers is 133. what are the... (answered by ewatrrr)