document.write( "Question 968243: Use differences to find a pattern in the sequence.
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Algebra.Com's Answer #591774 by Edwin McCravy(20056)\"\" \"About 
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document.write( "3, -2,  1, 18, 55, 118, 213\r\n" );
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document.write( "List them in a column, then form the differences to the right by\r\n" );
document.write( "subtracting each number from the one just below it\r\n" );
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document.write( "  3  -5   8  6\r\n" );
document.write( " -2   3  14  6\r\n" );
document.write( "  1  17  20  6\r\n" );
document.write( " 18  37  26  6\r\n" );
document.write( " 55  63  32\r\n" );
document.write( "118  95\r\n" );
document.write( "213\r\n" );
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document.write( "So we see that the 3rd differences are all 6's.\r\n" );
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document.write( "So we assume a 3rd degree polynomial general term:\r\n" );
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document.write( "\"An%5E3%2BBn%5E2%2BCn%2BD=a%5Bn%5D\"\r\n" );
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document.write( "There are 4 unknowns A,B,C,D so we will only need\r\n" );
document.write( "the first 4 terms.\r\n" );
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document.write( "We substitute n=1 and a1=3\r\n" );
document.write( "We substitute n=2 and a2=-2\r\n" );
document.write( "We substitute n=3 and a3=1\r\n" );
document.write( "We substitute n=4 and a4=18\r\n" );
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document.write( "So we have the system:\r\n" );
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document.write( "Solve by any method and get A=1, B=-2, C=-6, D=10\r\n" );
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document.write( "So the general equation is\r\n" );
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document.write( "\"a%5Bn%5D=n%5E3-2n%5E2-6n%2B10\"\r\n" );
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document.write( "Edwin

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