document.write( "Question 340070: What is the equation for this sequence?\r
\n" ); document.write( "\n" ); document.write( "1, 4, 9, 17, 29,...\r
\n" ); document.write( "\n" ); document.write( "I tried n(n-1) + n where n is the nth term, and that only works for the first three terms. \n" ); document.write( "

Algebra.Com's Answer #243725 by Edwin McCravy(20056) $\"\"$ $\"About$

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1, 4, 9, 17, 29,...
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document.write( "We make a difference table and see how many differences\r\n" );
document.write( "it takes before the differences are all the same:\r\n" );
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document.write( "1     4     9    17    29   <--- original sequence\r\n" );
document.write( "   3     5     8    12      <--- sequence of 1st differences \r\n" );
document.write( "      2     3     4         <--- sequence of 2nd differences\r\n" );
document.write( "         1     1            <--- sequence of 3rd differences\r\n" );
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document.write( "Since the 3rd difference are all the same, a 3rd degree equation\r\n" );
document.write( "will work. Let the 3rd degree equation be\r\n" );
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document.write( "We substitute the first 4 terms into that.\r\n" );
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document.write( "or\r\n" );
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document.write( "Do you know how to solve that system?  If not\r\n" );
document.write( "post again asking how. The solutions are\r\n" );
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document.write( "A = , B = 0, C = , D = -1\r\n" );
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document.write( "So the equation is\r\n" );
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document.write( "or we could get a common denominator and write it\r\n" );
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document.write( "Edwin

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