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 #547760 by Edwin McCravy(20056) $\"\"$ $\"About$

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document.write( "Let the five consecutive even integers be \r\n" );
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document.write( "2n, 2n+2, 2n+4, 2n+6, 2n+8\r\n" );
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document.write( "Let the five consecutive odd integers be \r\n" );
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document.write( "2k+1, 2k+3, 2k+5, 2k+7, 2k+9.\r\n" );
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document.write( "Assume, for contradiction, that their averages can be equal\r\n" );
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document.write( "If their averages are equal, then\r\n" );
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document.write( "Multiply both sides by 5\r\n" );
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document.write( "This cannot be, because the left side \r\n" );
document.write( "is even and the right side is odd.\r\n" );
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document.write( "This is a contradiction.\r\n" );
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document.write( "Therefore the answer is \"NO\", the average of 5 even integers \r\n" );
document.write( "can never be equal to the average of 5 odd integers.\r\n" );
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document.write( "Edwin

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