document.write( "Question 1209385: Let a_1, a_2, a_3, ... be an arithmetic sequence. Let S_n denote the sum of the first n terms. If S_{10} = 1 and S_{200} = 1/2, then find S_{15}. \n" ); document.write( "
Algebra.Com's Answer #848736 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "My ugly answer differs from Greenestamps' ugly answer, although we\r\n" );
document.write( "agree with the ugly first terms and common difference.

\n" ); document.write( "Let a_1, a_2, a_3, ... be an arithmetic sequence. Let S_n denote the sum of the
\n" ); document.write( "first n terms. If S_{10} = 1 and S_{200} = 1/2, then find S_{15}.
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document.write( "\"system%28%0D%0A%0D%0A1=5%282a%5B1%5D%2B9d%29%2C%0D%0A1%2F2=100%282a%5B1%5D%2B199d%29%29\"\r\n" );
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document.write( "\"system%28%0D%0A%0D%0A1=10a%5B1%5D%2B45d%2C%0D%0A1%2F2=200a%5B1%5D%2B19900d%29\"\r\n" );
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document.write( "\"system%28%0D%0A%0D%0A1=10a%5B1%5D%2B45d%2C%0D%0A1=400a%5B1%5D%2B39800d%29\"\r\n" );
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document.write( "Multiply the first equation by -40 so the a1 terms will cancel:\r\n" );
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document.write( "\"system%28%0D%0A%0D%0A-40=-400a%5B1%5D-1800d%2C%0D%0A1=400a%5B1%5D%2B39800d%29\"\r\n" );
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document.write( "\"-39=38000d\"\r\n" );
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document.write( "\"%28-39%29%2F38000=d\"\r\n" );
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document.write( "\"d=-39%2F38000\"\r\n" );
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document.write( "Go back to\r\n" );
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document.write( "\"system%28%0D%0A%0D%0A1=10a%5B1%5D%2B45d%2C%0D%0A1=400a%5B1%5D%2B39800d%29\"\r\n" );
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document.write( "Multiply the first equation by -7960 and the second equation by 9 so\r\n" );
document.write( "the terms in d will cancel.\r\n" );
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document.write( "\"system%28%0D%0A%0D%0A-7960=-79600a%5B1%5D-358200d%2C%0D%0A9=3600a%5B1%5D%2B358200d%29\"\r\n" );
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document.write( "\"-7951=-76000a%5B1%5D\"\r\n" );
document.write( "\"%28-7951%29%2F%28-76000%29=a%5B1%5D\"\r\n" );
document.write( "\"a%5B1%5D=7951%2F76000\"\r\n" );
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document.write( "Substituting in\r\n" );
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document.write( "\"S%5Bn%5D=expr%28n%2F2%29%282a%5B1%5D%2B%28n-1%29d%29\"\r\n" );
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document.write( "\"S%5Bn%5D=expr%28n%2F2%29%282%287951%2F76000%29%2B%28n-1%29%28-39%2F3800%29%29\"\r\n" );
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document.write( "\"S%5Bn%5D=expr%28n%2F2%29%287951%2F38000-%2839n%29%2F3800%2B39%2F3800%29%29\"\r\n" );
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document.write( "\"S%5Bn%5D=expr%28n%2F2%29%287951%2F38000-%28390n%29%2F38000%2B390%2F38000%29%29\"\r\n" );
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document.write( "\"S%5Bn%5D=expr%28n%2F2%29%28%288341-390n%29%2F38000%29\"\r\n" );
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document.write( "Now we'll substitute n=15\r\n" );
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document.write( "\"S%5B15%5D=expr%2815%2F2%29%28%288341-390%2815%29%29%2F38000%29\"\r\n" );
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document.write( "\"S%5B15%5D=expr%2815%2F2%29%28%288341-5850%29%2F38000%29\"\r\n" );
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document.write( "\"S%5B15%5D=expr%2815%2F2%29%282491%2F38000%29\"\r\n" );
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document.write( "\"S%5B15%5D=expr%283%2F2%29%282491%2F7600%29\"\r\n" );
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document.write( "\"S%5B15%5D=7473%2F15200\"\r\n" );
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document.write( "Edwin
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