SOLUTION: When filling in the table of values for y = x^2, I noticed the values of y differ by a series of odd numbers: if x = 0, 1, 2, 3, 4... then y = 0, 1, 4, 9, 16... the y values differ

Question 498634: When filling in the table of values for y = x^2, I noticed the values of y differ by a series of odd numbers: if x = 0, 1, 2, 3, 4... then y = 0, 1, 4, 9, 16... the y values differing by 1, 3, 5, 7... For y = (1/8)(x-4)^2 +5, the x values 4, 5, 6, 7... give y = 5, 5.125, 5.500, 6.125, 7... which works out to a difference of 1*(1/8), 3*(1/8), 5*(1/8), 7*(1/8)...
Why does this happen?
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
For the relation y = x^2, we can see that the difference between successive terms is (x+1)^2 - x^2, which is equal to 2x + 1. This turns out to be an arithmetic sequence with common difference 2, hence the 1, 3, 5, 7, ...
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