document.write( "Question 672674: A list of consecutive integers starting with 1 is written on the blackboard. One of the numbers is erased. If the average of the remaining numbers in 35 6/17, then the number erased was? \n" ); document.write( "

Algebra.Com's Answer #418279 by Edwin McCravy(20065) $\"\"$ $\"About$

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A list of consecutive integers starting with 1 is
\n" ); document.write( "written on the blackboard. One of the numbers is erased.
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document.write( "The average of a list of any number of consecutive integers\r\n" );
document.write( "is the average of the first and last numbers\r\n" );
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document.write( "The first number is 1.  Let the last number be n\r\n" );
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document.write( "Then the average would be \r\n" );
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document.write( "The average must be somewhere not too far from 35 6/17.\r\n" );
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document.write( "If the average were 36 then we would have:\r\n" );
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document.write( " = 36\r\n" );
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document.write( "1+n = 72\r\n" );
document.write( "  n = 71\r\n" );
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document.write( "Since the average is 36 6/17 then that denominator\r\n" );
document.write( "of 17 tells us that 1 less than the number of terms must \r\n" );
document.write( "have been a multiple of 17.  The nearest multiple of 17 to \r\n" );
document.write( "71 is 68.  So that means the number of terms is one more \r\n" );
document.write( "than that or 69.\r\n" );
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document.write( "The formula for the first n counting integers is \r\n" );
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document.write( "So the sum of the first 69 counting numbers is   = 2415\r\n" );
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document.write( "Let k be the number erased, then the average of the remaining\r\n" );
document.write( "68 terms is\r\n" );
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document.write( " = \r\n" );
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document.write( " =   \r\n" );
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document.write( "Multiplying both sides by 68\r\n" );
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document.write( "2415 - k = 2404\r\n" );
document.write( "      -k = -11\r\n" );
document.write( "       k = 11\r\n" );
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document.write( "So the term that was erased was 11.\r\n" );
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document.write( "Edwin

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