document.write( "Question 662463: Question: The arithmetic series 5 + 9 + 13 + ... + tn has a sum of 945. How many terms does the series have?\r
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Algebra.Com's Answer #412292 by Edwin McCravy(20056)\"\" \"About 
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document.write( "5 + 9 + 13 + ... + tn = 945\r\n" );
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document.write( "We need the sum formula:\r\n" );
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document.write( "Sn = \"n%2F2\"[2t1 + (n-1)·d]\r\n" );
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document.write( "To find d, the common difference, we subtract the first term,\r\n" );
document.write( "t1 = 5 from the second term t2 = 9, and\r\n" );
document.write( "get 9-5 = 4, and as a check we also subtract the second term,\r\n" );
document.write( "t2 = 9 from the third term t3 = 12, and\r\n" );
document.write( "get 13-9 = 4, so the common difference d is 4.  So we substitute\r\n" );
document.write( "d = 4, Sn = 945, t1 = 5 and solve for n:\r\n" );
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document.write( "Sn = \"n%2F2\"[2t1 + (n-1)·d]\r\n" );
document.write( "945 = \"n%2F2\"[2·5 + (n-1)·4]\r\n" );
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document.write( "Multiply both sides by 2 to clear the fraction on the right:\r\n" );
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document.write( "1890 = n[10 + (n-1)·4]\r\n" );
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document.write( "1890 = n[10 + 4(n-1)]\r\n" );
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document.write( "1890 = n[10 + 4n - 4]\r\n" );
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document.write( "1890 = n[4n + 6]\r\n" );
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document.write( "1890 = 4n² + 6n\r\n" );
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document.write( "Divide through by 2\r\n" );
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document.write( "945 = 2n² + 3n\r\n" );
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document.write( "Get 0 on the left\r\n" );
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document.write( "0 = 2n² + 3n - 945\r\n" );
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document.write( "The right side factors as\r\n" );
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document.write( "0 = (n - 21)(2n + 45)\r\n" );
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document.write( "Use the zero-factor property:\r\n" );
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document.write( "    n - 21 = 0;   2n + 45 = 0\r\n" );
document.write( "         n = 21;       2n = -45\r\n" );
document.write( "                        n = \"-45%2F2\"\r\n" );
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document.write( "Ignore the negative answer.\r\n" );
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document.write( "It has 21 terms.\r\n" );
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document.write( "5 + 9 + 13 + 17 + 21 + 25 + 29 + 33 + 37 + 41 + 45 + 49 + 53 + 57 + 61 + 65 + 69 + 73 + 77 + 81 + 85\r\n" );
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document.write( "Edwin
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