document.write( "Question 854950: The sum of 6 consecutive even numbers is 366. What is the third number in this sequence? \n" ); document.write( "

Algebra.Com's Answer #515019 by KMST(5328) $\"\"$ $\"About$

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If $\"n\"$ = the third number, the numbers are
\n" ); document.write( " $\"n-4\"$ , $\"n-2\"$ , $\"n\"$ , $\"n%2B2\"$ , $\"n%2B4\"$ , and $\"n%2B6\"$ .
\n" ); document.write( "Their sum is
\n" ); document.write( "

\n" ); document.write( " $\"6n%2B6=366\"$
\n" ); document.write( " $\"6n=366-6\"$
\n" ); document.write( " $\"6n=360\"$
\n" ); document.write( " $\"n=360%2F6\"$
\n" ); document.write( " $\"highlight%28n=60%29\"$
\n" ); document.write( "
\n" ); document.write( "NOTES:
\n" ); document.write( "1) The teacher may expect some talk about arithmetic sequences, but it is easy enough as done above.
\n" ); document.write( "2) As mental math (as I would do for a multiple choice test),
\n" ); document.write( "I know that the sum of consecutive terms in an arithmetic sequence is the average times the number of terms. That average would be $\"366%2F6=61\"$ . I also know that in an arithmetic sequence the average is the median, and with 6 terms that median would be halfway between the third and fourth terms, so the third and fourth terms should be 60 and 62.
\n" ); document.write( "3) If I read \"consecutive even numbers\" or \"consecutive odd numbers\", I simply call some convenient number $\"n\"$ (not caring if $\"n\"$ is odd or even until the end). I just make the consecutive even or odd numbers 2 units apart from one another. At the end, the results should be even or odd as required, or else the problem has no answer (or I made a mistake). \n" ); document.write( "

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