document.write( "Question 1100151: What is the average of 1,2,3,4,5,6,7,8,9...2017 in simplest form? I don't know where to start because there are just too many numbers too add and divide by. Could anybody help? \n" ); document.write( "

Algebra.Com's Answer #714640 by ikleyn(52909) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "The sequense in this post is an arithmetic progression with the first term 1, the common difference 1, the last term 2017  \r\n" );
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document.write( "and the number of terms 2017.\r\n" );
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document.write( "The sum of this progression is VERY WELL known: it is .\r\n" );
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document.write( "In order for to find \"the average\", you must to divide this sum by 2017, the number of terms.\r\n" );
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document.write( "Then you will get   = 1009 for the average.\r\n" );
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document.write( "Notice, that 2018 is the sum of the first and the last term of this progression.\r\n" );
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document.write( "It is not accidentally:\r\n" );
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document.write( "    The average of any arithmetic progression is the same as the average of its extreme terms.\r\n" );
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\n" ); document.write( "There is a bunch of lessons on arithmetic progressions in this site:\r
\n" ); document.write( "\n" ); document.write( "    - Arithmetic progressions\r
\n" ); document.write( "\n" ); document.write( "    - The proofs of the formulas for arithmetic progressions \r
\n" ); document.write( "\n" ); document.write( "    - Problems on arithmetic progressions \r
\n" ); document.write( "\n" ); document.write( "    - Word problems on arithmetic progressions\r
\n" ); document.write( "\n" ); document.write( "    - One characteristic property of arithmetic progressions\r
\n" ); document.write( "\n" ); document.write( "    - Solved problems on arithmetic progressions \r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic \"Arithmetic progressions\".\r
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\n" ); document.write( "\n" ); document.write( "Save the link to this textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-II
\n" ); document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "into your archive and use when it is needed.\r
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