document.write( "Question 1072952: given a1=28 an=-77 and sn =-196 in an A.P find the
\n" ); document.write( "10th term and the sum of the first 10 terms \n" ); document.write( "
Algebra.Com's Answer #687793 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"a%5B1%5D=28\"                <--first term\r\n" );
document.write( "\"a%5Bn%5D=a%5B1%5D%2B%28n-1%29d=-77\"   <--formula for nth term\r\n" );
document.write( "\"a%5Bn%5D=28%2B%28n-1%29d=-77\"\r\n" );
document.write( "\"28%2B%28n-1%29d=-77\"\r\n" );
document.write( "\"%28n-1%29d+=+-105\"\r\n" );
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document.write( "\"S%5Bn%5D=expr%28n%2F2%29%282a%5B1%5D%2B%28n-1%29d%29=+-196\"  <-- formula for nth term\r\n" );
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document.write( " Substitute for a1 and (n-1)d=-105\r\n" );
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document.write( "\"expr%28n%2F2%29%282%2828%29-105%29=+-196\"\r\n" );
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document.write( "\"expr%28n%2F2%29%2856-105%29=+-196\"\r\n" );
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document.write( "\"expr%28n%2F2%29%28-49%29=+-196\"\r\n" );
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document.write( "Multiply through by 2\r\n" );
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document.write( "\"n%28-49%29=+-392\"\r\n" );
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document.write( "\"n=%28-392%29%2F%28-49%29\"\r\n" );
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document.write( "\"n=8\"          <--number of terms whose sum is -77\r\n" );
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document.write( "We'll need d, so\r\n" );
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document.write( "\"%28n-1%29d=-105\"\r\n" );
document.write( "\"%288-1%29d=-105\"\r\n" );
document.write( "\"7d=-105\"\r\n" );
document.write( "\"d=-15\"        <-- common difference, d\r\n" );
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document.write( "To find 10th term:\r\n" );
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document.write( "\"a%5Bn%5D=a%5B1%5D%2B%28n-1%29d\"\r\n" );
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document.write( "Substitute n=10, a1 = 28, n=10, d=-15\r\n" );
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document.write( "\"a%5B10%5D=28%2B%2810-1%29%28-15%29\"\r\n" );
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document.write( "\"a%5B10%5D=28%2B9%28-15%29\"\r\n" );
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document.write( "\"a%5B10%5D=28-135\"\r\n" );
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document.write( "\"a%5B10%5D=-107\"     <-- 10th term\r\n" );
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document.write( "\"S%5Bn%5D=expr%28n%2F2%29%282a%5B1%5D%2B%28n-1%29d%29\" <-- formula for sum of first n terms\r\n" );
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document.write( "\"S%5B10%5D=expr%2810%2F2%29%282%2828%29%2B%2810-1%29%28-15%29%29\"\r\n" );
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document.write( "\"S%5B10%5D=%285%29%2856%2B%289%29%28-15%29%29\"\r\n" );
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document.write( "\"S%5B10%5D=%285%29%2856-135%29\"\r\n" );
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document.write( "\"S%5B10%5D=%285%29%28-79%29\"\r\n" );
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document.write( "\"S%5B10%5D=-395\"\r\n" );
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document.write( "Checking, the sequence is:\r\n" );
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document.write( "28,13,-2,-17,-32,-47,-62,-77,-92,-107\r\n" );
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document.write( "Add them\r\n" );
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document.write( "28+13-2-17-32-47-62-77-92-107 = -395\r\n" );
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document.write( "Add the first 8 terms\r\n" );
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document.write( "28+13-2-17-32-47-62-77 = -196\r\n" );
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document.write( "Everything checks.\r\n" );
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document.write( "Edwin
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