document.write( "Question 929822: answer for what is the sixteen term in the following sequence? 1,2,4,7,11,16,22
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Algebra.Com's Answer #564490 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Put them in a column.  Out beside each number write what\r\n" );
document.write( "you get whe you subtract each number from the one just below it.\r\n" );
document.write( "Then make a third column doing that with the second column\r\n" );
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document.write( " 1   1   1 \r\n" );
document.write( " 2   2   1\r\n" );
document.write( " 4   3   1\r\n" );
document.write( " 7   4   1\r\n" );
document.write( "11   5   1\r\n" );
document.write( "16   5\r\n" );
document.write( "22\r\n" );
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document.write( "Those columns are called the first and second differences.\r\n" );
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document.write( "Since it takes 2 columns of differences to get a column that has \r\n" );
document.write( "all the same number, we assume a polynomial of degree 2 for the \r\n" );
document.write( "nth term .\r\n" );
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document.write( "Substitute n=1\r\n" );
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document.write( "and since the first term is 1, we can write\r\n" );
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document.write( " or\r\n" );
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document.write( "Substitute n=2\r\n" );
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document.write( "and since the second term is 2, we can write\r\n" );
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document.write( " or\r\n" );
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document.write( "Substitute n=3\r\n" );
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document.write( "and since the third term is 4, we can write\r\n" );
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document.write( " or\r\n" );
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document.write( "Now we have a system of equations\r\n" );
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document.write( "Solve that system and get ,,\r\n" );
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document.write( "So the nth term,\r\n" );
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document.write( "  \r\n" );
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document.write( "becomes\r\n" );
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document.write( "or if you prefer you can get an LCD\r\n" );
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document.write( "Then for the 16th term, we substitute n=16\r\n" );
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document.write( " =  = \r\n" );
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document.write( "Checking:\r\n" );
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document.write( "1,2,4,7,11,16,22,29,37,46,56,67,79,92,106,121\r\n" );
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document.write( "Edwin

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