document.write( "Question 1129010: Nth term of -7,-6,-3,2,9,18,29 \n" ); document.write( "
Algebra.Com's Answer #745560 by Edwin McCravy(20056)\"\" \"About 
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Nth term of -7,-6,-3,2,9,18,29
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document.write( "List in a column. Subtract each number\r\n" );
document.write( "from the number under it, and place this\r\n" );
document.write( "difference to the right of each number in\r\n" );
document.write( "a new column to the right:\r\n" );
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document.write( "-7  1\r\n" );
document.write( "-6  3\r\n" );
document.write( "-3  5\r\n" );
document.write( " 2  7\r\n" );
document.write( " 9  9\r\n" );
document.write( "18 11\r\n" );
document.write( "29\r\n" );
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document.write( "Do the same with the second column column\r\n" );
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document.write( "-7  1  2\r\n" );
document.write( "-6  3  2\r\n" );
document.write( "-3  5  2\r\n" );
document.write( " 2  7  2\r\n" );
document.write( " 9  9  2\r\n" );
document.write( "18 11\r\n" );
document.write( "29\r\n" );
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document.write( "It takes 2 additional columns to get a column that contains only\r\n" );
document.write( "one number.  So we expect a 2nd degree equation for the\r\n" );
document.write( "nth term.  So we will assume an equation of this form:\r\n" );
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document.write( "nth term = tn = An² + Bn + C \r\n" );
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document.write( "Then we substitute 1,2 and 3.\r\n" );
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document.write( "1st term = t1 = A(1)² + B(1) + C = A + B + C = -7\r\n" );
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document.write( "2nd term = t2 = A(2)² + B(2) + C = 4A + 2B + C = -6\r\n" );
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document.write( "3rd term = t3 = A(3)² + B(3) + C = 9A + 3B + C = -3\r\n" );
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document.write( "So we have this system of 3 equations in 3 unknowns:\r\n" );
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document.write( " A +  B + C = -7\r\n" );
document.write( "4A + 2B + C = -6\r\n" );
document.write( "9A + 3B + C = -3\r\n" );
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document.write( "Solve that system of equations and get A = 1, B=-2 and c=-6\r\n" );
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document.write( "So the nth term tn = An² + Bn + C becomes:\r\n" );
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document.write( "nth term = tn = n² - 2n - 6  \r\n" );
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document.write( "Edwin
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