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):
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
