SOLUTION: A class is working on finding patterns among the counting numbers. A student noticed an interesting pattern. She said that if you take 3 consecutive counting numbers (e.g. 7,8&9)
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Question 626170: A class is working on finding patterns among the counting numbers. A student noticed an interesting pattern. She said that if you take 3 consecutive counting numbers (e.g. 7,8&9) and square the middle number (8 squared) then the resulting number (64) is one larger than the product of the two other numbers (i.e 64 is one greater that 7 x 9 = 63). Is this true for all sets of three consecutive numbers?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Let 
represent the middle number of any given set of three consecutive positive integers. Then the smaller number of the three is 
and the larger is 
. The square of the middle number is 
and the product of the smaller and the larger is 
.
Note, this is true for all integers, not just the positive integers (what you are calling the "counting numbers")
John
My calculator said it, I believe it, that settles it
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