document.write( "Question 1143335: Looking for a missing number in the interior of a sequence and can't figure out how to get there.\r
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Algebra.Com's Answer #764126 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "There will always an infinite number of polynomial sequences which\r\n" );
document.write( "any subsequence of numbers will fit.  I hope your teacher knows that!\r\n" );
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document.write( "The first three numbers \r\n" );
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document.write( "1, 4, 27, for the sequence are 11, 22, 33,\r\n" );
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document.write( "so the fourth term should be 44 or 256, and the 5th term\r\n" );
document.write( "should be 55 or 3125, but there is no way it can be the 3761,\r\n" );
document.write( "which is a prime number.\r\n" );
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document.write( "So let's find one polynomial sequence it could be. We make this\r\n" );
document.write( "difference table, where the first column is the given sequence.\r\n" );
document.write( "Then immediately to the right of each number is that number\r\n" );
document.write( "subtracted from what's immediately under it, (if there is a\r\n" );
document.write( "number immediately under it.)\r\n" );
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document.write( "   1       3        20      70-X   3908-4x  \r\n" );
document.write( "   4      23      X-50   3838-3X  \r\n" );
document.write( "  27    X-27   3788-2X\r\n" );
document.write( "   X  3761-X     \r\n" );
document.write( "3761\r\n" );
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document.write( "So we let 3908-4x = 0\r\n" );
document.write( "              -4x = -3908\r\n" );
document.write( "                x = 977\r\n" );
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document.write( "Then that makes a nice looking sequence, since 977 is\r\n" );
document.write( "about the proper looking size.\r\n" );
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document.write( "1, 4, 27, 977, 3761\r\n" );
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document.write( "That sequence has the nth term:\r\n" );
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document.write( "\"a%5Bn%5D+=+-54x%5E3%2Bexpr%284471%2F6%29n%5E2-3111n%2Bexpr%289815%2F6%29n-2509\"\r\n" );
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document.write( "But there are an infinite number of other possibilities.\r\n" );
document.write( "In fact you can pick any number for X and there will be\r\n" );
document.write( "an infinite number of possibilities.  I suppose you are\r\n" );
document.write( "supposed to find the simplest one.  How is that supposed\r\n" );
document.write( "to be done?  If your teacher tell you how, please tell us, \r\n" );
document.write( "for we have no idea, although we have advanced degrees in\r\n" );
document.write( "mathematics.\r\n" );
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document.write( "Edwin
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