document.write( "Question 1191256: What is the first of 100 consecutive odd integers whose sum is 100^100? \n" ); document.write( "
Algebra.Com's Answer #823057 by ikleyn(52817)\"\" \"About 
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\n" ); document.write( "What is the first of 100 consecutive odd integers whose sum is 100^100?
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document.write( "Let the first term be  \"a%5B1%5D\".\r\n" );
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document.write( "Then the 100-th term is  \"a%5B1%5D%2B2%2A99\".\r\n" );
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document.write( "The average of the first and the 100-th term is  \"%28a%5B1%5D%2B%28a%5B1%5D%2B2%2A99%29%29%2F2\" = \"a%5B1%5D%2B99\".\r\n" );
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document.write( "The sum of this sequence must be  \"100%5E100\",  which gives this equation\r\n" );
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document.write( "    \"%28a%5B1%5D%2B99%29%2A100\" = \"100%5E100\".\r\n" );
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document.write( "It implies  \"a%5B1%5D\" = \"100%5E99+-+99\".    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "For introductory lessons on arithmetic progressions see \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( "in this site.\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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