document.write( "Question 158587: im confused on how rto wokr this sequence out
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Algebra.Com's Answer #116821 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
I'm confused on how to work this sequence out
\n" ); document.write( " 0, 14, 52, 126, 248
\n" ); document.write( "I have tried n cubed but cannot find the answer?\r
\n" ); document.write( "\n" ); document.write( "\"t%5B1%5D=0\", \"t%5B2%5D=14\", \"t%5B3%5D=52\", \"t%5B4%5D=126\", \"t%5B5%5D=248\"
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document.write( "First we make a difference table by subtracting \r\n" );
document.write( "each adjacent pair, placing the difference between\r\n" );
document.write( "and below each pair.  Then doing the same thing\r\n" );
document.write( "again until the numbers are all the same:\r\n" );
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document.write( "         0     14     52   126   248 \r\n" );
document.write( "            14     38    74   122  \r\n" );
document.write( "               24     36    48 \r\n" );
document.write( "                   12    12\r\n" );
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document.write( "It takes 3 lines before the differences are the same, 12.\r\n" );
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document.write( "Therefore we must assume a 3rd degree polynomial:\r\n" );
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document.write( "\"t%5Bn%5D+=+An%5E3+%2B+Bn%5E2+%2B+Cn+%2B+D\"\r\n" );
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document.write( "When n = 1:\r\n" );
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document.write( "\"t%5B1%5D+=+A%281%29%5E3+%2B+B%281%29%5E2+%2B+C%281%29+%2B+D\"\r\n" );
document.write( "\"0+=+A+%2B+B+%2B+C+%2B+D\"\r\n" );
document.write( "\"A+%2B+B+%2B+C+%2B+D=0\"\r\n" );
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document.write( "When n = 2:\r\n" );
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document.write( "\"t%5B2%5D+=+A%282%29%5E3+%2B+B%282%29%5E2+%2B+C%282%29+%2B+D\"\r\n" );
document.write( "\"14+=+8A+%2B+4B+%2B+2C+%2B+D\"\r\n" );
document.write( "\"8A+%2B+4B+%2B+2C+%2B+D=14\"\r\n" );
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document.write( "When n = 3:\r\n" );
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document.write( "\"t%5B3%5D+=+A%283%29%5E3+%2B+B%283%29%5E2+%2B+C%283%29+%2B+D\"\r\n" );
document.write( "\"52+=+27A+%2B+9B+%2B+3C+%2B+D\"\r\n" );
document.write( "\"27A+%2B+9B+%2B+3C+%2B+D=52\"\r\n" );
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document.write( "When n = 4:\r\n" );
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document.write( "\"t%5B4%5D+=+A%284%29%5E3+%2B+B%284%29%5E2+%2B+C%284%29+%2B+D\"\r\n" );
document.write( "\"126+=+64A+%2B+16B+%2B+4C+%2B+D\"\r\n" );
document.write( "\"64A+%2B+16B+%2B+4C+%2B+D=126\" \r\n" );
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document.write( "Do you know how to solve a system of\r\n" );
document.write( "4 equations in 4 unknowns? If not post again\r\n" );
document.write( "asking how.\r\n" );
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document.write( "Answer:  \"A=2\", \"B=0\", \"C=0\", \"D=-2\"\r\n" );
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document.write( "So \"t%5Bn%5D+=+An%5E3+%2B+Bn%5E2+%2B+Cn+%2B+D\" becomes\r\n" );
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document.write( "\"t%5Bn%5D+=+2n%5E3+%2B+0n%5E2+%2B+0n+-+2\" or\r\n" );
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document.write( "\"t%5Bn%5D+=+2n%5E3+-2\"\r\n" );
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document.write( "Edwin
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