document.write( "Question 903078: Is the average of 5consecutive even numbers equal to the average of 5 consecutive odd numbers. \n" ); document.write( "

Algebra.Com's Answer #547764 by solver91311(24713) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "No.\r
\n" ); document.write( "\n" ); document.write( "Let

represent an arbitrary even integer. Then

is the next consecutive even integer.

is the next after that, and so on. The sum of five consecutive even integers is then

, and the average is then that sum divided by 5, namely

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\n" ); document.write( "\n" ); document.write( "Similarly, if

is an arbitrary odd integer, the sum of five consecutive odd integers would be

and the average would be

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\n" ); document.write( "\n" ); document.write( "In order for there to be a set of five consecutive even integers that have an average equal to the average of a set of five consecutive odd integers, then the statement:\r
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\n" ); document.write( "\n" ); document.write( "must be true and therefore\r
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\r
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\n" ); document.write( "\n" ); document.write( "must be true.\r
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\n" ); document.write( "\n" ); document.write( "Since there is no even integer that is equal to an odd integer, this relation can never be true. Hence, a set of 5 consecutive even integers whose average is equal to the average of a set of 5 consecutive odd integers does not exist.
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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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