document.write( "Question 530099: Find the largest of three consecutive odd integers, such that 3 times the middle integer is 1 more than the sum of the first and third \n" ); document.write( "

Algebra.Com's Answer #349895 by KMST(5328) $\"\"$ $\"About$

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For 3 consecutive odd integers, the sum of the first and third equals twice the middle one.
\n" ); document.write( "The same would be true for 3 consecutive integers, or for 3 consecutive even integers, or ...
\n" ); document.write( "Back to the problem.
\n" ); document.write( "Let the middle integer be $\"n\"$
\n" ); document.write( "We know that 3 times the middle one is $\"3n\"$
\n" ); document.write( "We know that the sum of the largest and smallest is $\"2n\"$
\n" ); document.write( "The problem says that
\n" ); document.write( " $\"3n=2n%2B1\"$
\n" ); document.write( "That means that $\"n=1\"$ , and the 3 consecutive odd integers are
\n" ); document.write( "-1, 1, and 3.
\n" ); document.write( "The fact that one of them is negative is odd indeed, but -1 is certainly an integer, and I guess it still qualifies as an odd number. It does not divide evenly by 2.
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