document.write( "Question 1178119: An infinite increasing list of numbers has the property that the median of the
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Algebra.Com's Answer #807304 by Edwin McCravy(20065)\"\" \"About 
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An infinite increasing list of numbers has the property that the median of
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document.write( "Let the first 3 terms be a,b,c, where a < b < c. the median is b.\r\n" );
document.write( "There are 3 terms, the 3rd odd integer is 5, so b=5.\r\n" );
document.write( "The sequence so far is a,5,c.  \r\n" );
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document.write( "Let the first 4 terms be a,5,c,d where a < 5 < c < d. the median is (5+c)/2.\r\n" );
document.write( "There are 4 terms, the 4th odd integer is 7, so \r\n" );
document.write( "(5+c)/2=7\r\n" );
document.write( "    5+c=14\r\n" );
document.write( "      c=9\r\n" );
document.write( "The sequence so far is a,5,9,d.\r\n" );
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document.write( "Let the first 5 terms be a,5,9,d,e where a < b < c < d < e. the median is 9.\r\n" );
document.write( "There are 5 terms, the 5th odd integer is 9.\r\n" );
document.write( "The sequence so far is a,5,9,d,e.\r\n" );
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document.write( "Let the first 6 terms be a,5,9,d,e,f where a < b < c < d < e < f. the median\r\n" );
document.write( "is (9+d)/2. There are 6 terms, the 6th odd integer is 11.\r\n" );
document.write( "(9+d)/2=11\r\n" );
document.write( "    9+d=22\r\n" );
document.write( "      d=13\r\n" );
document.write( "The sequence so far is a,5,9,13,e,f.\r\n" );
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document.write( "We guess from the middle 3 terms that the sequence is the arithmetic\r\n" );
document.write( "sequence 1,5,9,13,17,21,...\r\n" );
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document.write( "If so, the nth term is\r\n" );
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document.write( "\"a%5Bn%5D=a%5B1%5D%2B%28n-1%29D\", where a1 = 1, D = 4\r\n" );
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document.write( "\"a%5Bn%5D=1%2B%28n-1%294\"\r\n" );
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document.write( "So we set \r\n" );
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document.write( "\"a%5Bn%5D=1%2B%28n-1%294%3C2018\"\r\n" );
document.write( "\"1%2B%28n-1%294%3C2018\"\r\n" );
document.write( "\"1%2B4%28n-1%29%3C2018\"\r\n" );
document.write( "\"1%2B4n-4%3C2018\"\r\n" );
document.write( "\"4n-3%3C2018\"\r\n" );
document.write( "\"4n%3C2021\"\r\n" );
document.write( "\"n%3C505.25\"\r\n" );
document.write( "\"n%3C=505\"\r\n" );
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document.write( "So there are 505 numbers in the list less than 2018.\r\n" );
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document.write( "Edwin
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