SOLUTION: The given consecutive integers are 4,5, and 6. If I square the 2nd integer, the answer will be 25. Then, if I multiply the 1st and 3rd integer, the answer will be 24, Which is 1 nu

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: The given consecutive integers are 4,5, and 6. If I square the 2nd integer, the answer will be 25. Then, if I multiply the 1st and 3rd integer, the answer will be 24, Which is 1 nu      Log On


   

Question 772378: The given consecutive integers are 4,5, and 6. If I square the 2nd integer, the answer will be 25. Then, if I multiply the 1st and 3rd integer, the answer will be 24, Which is 1 number less that the squared integer. That happens every time I do the same method in consecutive integers. How is that possible?
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Interesting question!
Try to generalize and try the same process.

Three consecutive integers, n, n+1, n+2.


SQUARE THE SECOND INTEGER.
%28n%2B1%29%5E2
n%5E2%2B2n%2B1

MULTIPLY THE FIRST AND THIRD INTEGERS.
n%28n%2B2%29
n%5E2%2B2n

FIND THE DIFFERENCE BETWEEN THOSE TWO RESULTS.


n can be ANY integer. The process will still work.