document.write( "Question 786119: The arithmetic series 3+7+11+15+...is given.
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Algebra.Com's Answer #477830 by Edwin McCravy(20056)\"\" \"About 
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document.write( "7-3 = 4, 11=7 = 4, 15 - 11 = 4, so common difference -= d = 4\r\n" );
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document.write( "Sn = \"n%2F2\"[2a1 + (n-1)d]\r\n" );
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document.write( "where a1 = first term = 3.\r\n" );
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document.write( "Sn = \"n%2F2\"[2a1 + (n-1)d] < 500\r\n" );
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document.write( "                \"n%2F2\"[2(3) + (n-1)(4)] < 500\r\n" );
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document.write( "Multiply both sides by 2 to get rid of the fraction:\r\n" );
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document.write( "                 n[2(3) + (n-1)(4)] < 1000\r\n" );
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document.write( "                      n[6 + 4(n-1)] < 1000\r\n" );
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document.write( "                      n[6 + 4n - 4] < 1000\r\n" );
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document.write( "                          n[2 + 4n] < 1000\r\n" );
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document.write( "                           2n + 4nē < 1000\r\n" );
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document.write( "Divide through by 2\r\n" );
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document.write( "                            n + 2nē < 500  \r\n" );
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document.write( "Get 0 on the right and arrange terms on the left in\r\n" );
document.write( "descending order:\r\n" );
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document.write( "                      2nē + n - 500 < 0 \r\n" );
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document.write( "Using the quadratic formula we see that this has critical \r\n" );
document.write( "values approximately 15.6 and -16.1\r\n" );
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document.write( "We ignore the negative critical value and take the largest integer \r\n" );
document.write( "that does not exceed 15.1, which is 15.\r\n" );
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document.write( "So the first 15 terms have a sum less than 500.\r\n" );
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document.write( "answer = 15\r\n" );
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document.write( "Checking:\r\n" );
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document.write( "3+7+11+15+19+23+27+31+35+39+43+47+51+55+59 = 465\r\n" );
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document.write( "The 16th term would be 63, which would give a sum 528, which is over 500,\r\n" );
document.write( "so\r\n" );
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document.write( "answer = 15 is true. \r\n" );
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document.write( "Edwin
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