document.write( "Question 852459: 22,59,120,_,358.
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Algebra.Com's Answer #515276 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Since we have 4 terms, we will assume a third degree \r\n" );
document.write( "polynomial for the nth term, because a third degree polynomial\r\n" );
document.write( "has four coefficients.\r\n" );
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document.write( "That is, we assume a virtual function of the form\r\n" );
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document.write( "Y = A*N^3+B*N^2+C*N+D\r\n" );
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document.write( "Substitute these for (N,Y) (1,22), (2,59), (3,120), and (5,358)\r\n" );
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document.write( "    A*1^3+B*1^2+C*1+D = 22\r\n" );
document.write( "    A*2^3+B*2^2+C*2+D = 22\r\n" );
document.write( "    A*3^3+B*3^2+C*3+D = 22\r\n" );
document.write( "    A*5^3+B*5^2+C*5+D = 358\r\n" );
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document.write( "And solve the augmented matrix:\r\n" );
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document.write( "We solve that matrix and get \r\n" );
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document.write( "A = 1.83333333\r\n" );
document.write( "B = 1\r\n" );
document.write( "C = 21.16666667\r\n" );
document.write( "D = -2\r\n" );
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document.write( "Then we substitute X=4 in\r\n" );
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document.write( "Y = A*N^3+B*N^2+C*N+D\r\n" );
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document.write( "and get 216.\r\n" );
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document.write( "Edwin
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