document.write( "Question 572645: Use the Method of Finite Differences to find a function for the following sequences. 2.5, 6, 13.5, 25 \n" ); document.write( "
Algebra.Com's Answer #368480 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "n   tn    D1  D2\r\n" );
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document.write( "1   2.5  3.5  4\r\n" );
document.write( "2   6.0  7.5  4\r\n" );
document.write( "3  13.5 11.5\r\n" );
document.write( "4  25.0\r\n" );
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document.write( "Since it took 2 differences to get to a column that only\r\n" );
document.write( "had the same number in it, we can assume a 2nd degree\r\n" );
document.write( "polynomial function for tn of the form:\r\n" );
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document.write( "tn =  An² + Bn + C\r\n" );
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document.write( "Substituting\r\n" );
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document.write( "t1 =  A(1)² + B(1) + C\r\n" );
document.write( "2.5 = A(1) + B(1) + C\r\n" );
document.write( "2.5 = A + B + C\r\n" );
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document.write( "t2 =  A(2)² + B(2) + C\r\n" );
document.write( "6.0 = A(4) + B(2) + C\r\n" );
document.write( "6.0 = 4A + 2B + C\r\n" );
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document.write( "t3 =  A(3)² + B(3) + C\r\n" );
document.write( "13.5 = A(9) + B(3) + C\r\n" );
document.write( "13.5 = 9A + 3B + C\r\n" );
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document.write( "So we have this system\r\n" );
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document.write( "  2.5 = A +  B + C\r\n" );
document.write( " 6.0 = 4A + 2B + C\r\n" );
document.write( "13.5 = 9A + 3B + C\r\n" );
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document.write( "or maybe you would write it this way:\r\n" );
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document.write( " A +  B + C =  2.5\r\n" );
document.write( "4A + 2B + C =  6.0\r\n" );
document.write( "9A + 3B + C = 13.5\r\n" );
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document.write( "Solve that system of 3 equations in three\r\n" );
document.write( "unknowns and get:\r\n" );
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document.write( "A = 2, B = -2.5, C = 3\r\n" );
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document.write( "So the function \r\n" );
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document.write( "tn =  An² + Bn + C\r\n" );
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document.write( "becomes\r\n" );
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document.write( "tn =  2n² - 2.5n + 3\r\n" );
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document.write( "Edwin
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