document.write( "Question 934675: what number question mark refers in the series 3,9,17,?,43 \n" ); document.write( "
Algebra.Com's Answer #567672 by Edwin McCravy(20059)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Let x be the missing number.\r\n" );
document.write( "Make a table of differences by listing \r\n" );
document.write( "the terms in a column.  Then subtract\r\n" );
document.write( "each number from the number just below\r\n" );
document.write( "it.  Do this with each column until\r\n" );
document.write( "there are just 2 in the last column:\r\n" );
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document.write( "       1st     2nd      3rd \r\n" );
document.write( "an    diff    diff     diff\r\n" );
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document.write( " 3       6       2     x+27 \r\n" );
document.write( " 9       8    x-25    85-3x\r\n" );
document.write( "17    x-17   2x-60\r\n" );
document.write( " x    43-x\r\n" );
document.write( "43\r\n" );
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document.write( "Then set those two 3rd differences equal:\r\n" );
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document.write( "x+27 = 85-3x\r\n" );
document.write( "  4x = 112\r\n" );
document.write( "   x = 28\r\n" );
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document.write( "Answer: 28\r\n" );
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document.write( "-----------------------------\r\n" );
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document.write( "To find the general term:\r\n" );
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document.write( "Assume\r\n" );
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document.write( "\"a%5Bn%5D=An%5E3%2BBn%5E2%2BCn%2BD\"\r\n" );
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document.write( "Then, substituting n=1,2,3,5 and the \r\n" );
document.write( "4 sequence values gives us this system\r\n" );
document.write( "of equations:\r\n" );
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document.write( "\"A%2BB%2BC%2BD=3%2C8A%2B4B%2B2C%2BD=9%2C27A%2B9B%2B3C%2BD=17%2C125A%2B25B%2B5C%2BD=43%29\"\r\n" );
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document.write( "Solve that system and get \"A=1%2F6\", \"B=0\", \"C=29%2F6\", \"D=-2\"\r\n" );
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document.write( "\"a%5Bn%5D=expr%281%2F6%29n%5E3%2Bexpr%2829%2F6%29n-2\"  <---general term\r\n" );
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document.write( "Substituting \"n=3\" gives \"a%5B4%5D=28\". \r\n" );
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document.write( "Edwin
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