document.write( "Question 141060: The 15th term of an arithmetic series is 52, and the sum of the first 15 terms is 405. Find the first term of the series.\r
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Algebra.Com's Answer #102722 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
The 15th term of an arithmetic series is 52, and the sum of the first 15 terms is 405. Find the first term of the series.
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document.write( "Your book may use the letter \"a\" where I use the letter \"t\".\r\n" );
document.write( "Some books use \"t\" and some \"a\".\r\n" );
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document.write( "Given: n=15, t15 = 52,  S15 = 405\r\n" );
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document.write( "You need two formulas.\r\n" );
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document.write( "1. The nth term of an arithmetic series is given by the formula\r\n" );
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document.write( "   tn = t1 + (n-1)d\r\n" );
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document.write( "2. The sum of the first n terms of an arithmetic series is given by\r\n" );
document.write( "   the formula\r\n" );
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document.write( "   Sn = \"n%2F2\"[2t1 + (n-1)d]\r\n" );
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document.write( "Substituting in the first formula:\r\n" );
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document.write( "   t15 = t1 + (15-1)d\r\n" );
document.write( "     52 = t1 + 14d\r\n" );
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document.write( "Substituting in the second formula:\r\n" );
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document.write( "   S15 = \"15%2F2\"[2t1 + (15-1)d]\r\n" );
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document.write( "    405 = \"15%2F2\"(2t1 + 14d)\r\n" );
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document.write( "Clear of fractions by multiplying both sides by 2\r\n" );
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document.write( "    810 = 15(2t1 + 14d)\r\n" );
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document.write( "Divide both sides by 15\r\n" );
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document.write( "     54 = 2t1 + 14d\r\n" );
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document.write( "So you have this system of equations:\r\n" );
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document.write( "     52 = t1 + 14d\r\n" );
document.write( "     54 = 2t1 + 14d\r\n" );
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document.write( "Can you solve that system using substitution\r\n" );
document.write( "or elimination?  If not post again asking how.\r\n" );
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document.write( "Answer:       t1 = 2. d = 25/7  \r\n" );
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document.write( "Edwin

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