document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #394015 by solver91311(24713) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "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

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\n" ); document.write( "\n" ); document.write( "Note, this is true for all integers, not just the positive integers (what you are calling the \"counting numbers\")\r
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\n" ); document.write( "\n" ); document.write( "John
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\n" ); document.write( "My calculator said it, I believe it, that settles it
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$\"The$

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