document.write( "Question 154292: What number is next in the series? 10,4,3,11,15... \n" ); document.write( "
Algebra.Com's Answer #113685 by Edwin McCravy(20056)\"\" \"About 
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What number is next in the series? 10,4,3,11,15...\r
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document.write( "First of all that is not a series. It is a sequence.\r\n" );
document.write( "It would be a series if it had + signs between them,\r\n" );
document.write( "like this 10+4+3+11+15+...\r\n" );
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document.write( "But assuming they meant \"sequence\", I'll have to ask you a question. \r\n" );
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document.write( "Did you make a typo and the first number should have been 1, not 10?\r\n" );
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document.write( "If the first number had been 1, then we would have this pattern:\r\n" );
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document.write( "\"ONE\" is the smallest counting number that is spelled with 3 letters.\r\n" );
document.write( "\"FOUR\" is the smallest counting number that is spelled with 4 letters.\r\n" );
document.write( "\"THREE\" is the smallest counting number that is spelled with 5 letters.\r\n" );
document.write( "\"ELEVEN\" is the smallest counting number that is spelled with 6 letters.\r\n" );
document.write( "\"FIFTEEN\" is the smallest counting number that is spelled with 7 letters.\r\n" );
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document.write( "then for the next term, we could say:\r\n" );
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document.write( "\"THIRTEEN\" is the smallest counting number that is spelled with 8 letters.\r\n" );
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document.write( "Trouble is, 1 is not the first term, but 10 is.  Now, \"ten\" is spelled with\r\n" );
document.write( "3 letters, just as \"one\" is.  However 10 ruins the pattern from the very start\r\n" );
document.write( "because it's not the SMALLEST counting number spelled with 3 letters.\r\n" );
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document.write( "That means the next number in the sequence after 15, could be 13, 14, or 19,\r\n" );
document.write( "since those are all spelled with 8 letters. And with the \"ten\" being first\r\n" );
document.write( "instead of \"one\", there can be no requirement that it be the smallest integer\r\n" );
document.write( "spelled with 8 letters.\r\n" );
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document.write( "Maybe you intended for the sequence to be 1,4,3,11,15.  If so, 13 is the\r\n" );
document.write( "answer. Otherwise it could be 13, 14, or 19.\r\n" );
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document.write( "Now here is a formula for a sequence that has those first five terms:\r\n" );
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document.write( "\"a%5Bn%5D=%28-17n%5E4%2B186n%5E3-631n%5E2%2B702n%29%2F24\"\r\n" );
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document.write( "Here \"a%5B1%5D+=+10\"\r\n" );
document.write( "     \"a%5B2%5D+=++4\"\r\n" );
document.write( "     \"a%5B3%5D+=++3\" \r\n" );
document.write( "     \"a%5B4%5D+=+11\"   \r\n" );
document.write( "     \"a%5B5%5D+=+15\"\r\n" );
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document.write( "Then \"a%5B6%5D+=-15\" \r\n" );
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document.write( "That will do. But I think you may have mistyped a\r\n" );
document.write( "10 for a 1.  If so. then the next term is 13.\r\n" );
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document.write( "Edwin
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