document.write( "Question 1164687: NEED HELP
\n" ); document.write( "How do I make a formula for an increasingly decreasing sequence?
\n" ); document.write( "eg: 50,49,47,44,40,35,...
\n" ); document.write( "and how do I find the next three terms of the sequence? \n" ); document.write( "
Algebra.Com's Answer #789107 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
50,49,47,44,40,35,...
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document.write( "Make the set of first and second differences\r\n" );
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document.write( "50  49  47  44  40  35\r\n" );
document.write( "  -1  -2  -3  -4  -5\r\n" );
document.write( "    -1  -1  -1  -1  \r\n" );
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document.write( "and since the second differences are constant, we\r\n" );
document.write( "assume a 2nd degree polynomial in n for the general term:\r\n" );
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document.write( "[If the kth differences are constant, the the general term\r\n" );
document.write( "will be a polynomial in n of degree k.\r\n" );
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document.write( "\"a%5Bn%5D=An%5E2%2BBn%2BC\"\r\n" );
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document.write( "Then we substitute the first 3 terms for a1, a2, a3 and 1,2,3 for n\r\n" );
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document.write( "or\r\n" );
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document.write( "\"system%28A%2BB%2BC=50%2C4A%2B2B%2BC=49%2C9A%2B3B%2BC=47%29\"\r\n" );
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document.write( "Solve that system and get \r\n" );
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document.write( "A = -1/2, B = 1/2, and C = 50\r\n" );
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document.write( "So the general term is\r\n" );
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document.write( "\"a%5Bn%5D=expr%28-1%2F2%29n%5E2%2Bexpr%281%2F2%29n%2B50\"\r\n" );
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document.write( "You can find the next three terms either by extending the\r\n" );
document.write( "difference table:\r\n" );
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document.write( "50  49  47  44  40  35  29  22  14\r\n" );
document.write( "  -1  -2  -3  -4  -5  -6  -7  -8  \r\n" );
document.write( "    -1  -1  -1  -1  -1  -1  -1\r\n" );
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document.write( "or by substituting 7, 8, and 9 in the general formula:\r\n" );
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document.write( "\"a%5Bn%5D=expr%28-1%2F2%29n%5E2%2Bexpr%281%2F2%29n%2B50\"\r\n" );
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document.write( "\"a%5B7%5D=expr%28-1%2F2%297%5E2%2Bexpr%281%2F2%297%2B50=29\"\r\n" );
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document.write( "\"a%5B8%5D=expr%28-1%2F2%298%5E2%2Bexpr%281%2F2%298%2B50=22\"\r\n" );
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document.write( "\"a%5B9%5D=expr%28-1%2F2%299%5E2%2Bexpr%281%2F2%299%2B50=14\"\r\n" );
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document.write( "Edwin

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