document.write( "Question 1164133: What is the recursive formula of 4, 4¼, 4½, 5
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Algebra.Com's Answer #788425 by Edwin McCravy(20065)\"\" \"About 
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document.write( "4, 4¼, 4½, 5\r\n" );
document.write( "4, 4.25, 4.5, 5\r\n" );
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document.write( "\"a%5Bn%5D=p%2Aa%5Bn-1%5D%2Bq%2Aa%5Bn-2%5D\",  a(1)=4, a(2)=4.25, n=3,4,5,...\r\n" );
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document.write( " \"a%5B3%5D=p%2Aa%5B2%5D%2Bq%2Aa%5B1%5D\"\r\n" );
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document.write( "\"4.5=p%2A4.25%2Bq%2A4\"\r\n" );
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document.write( "\"a%5B4%5D=p%2Aa%5B3%5D%2Bq%2Aa%5B2%5D\"\r\n" );
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document.write( "\"5=p%2A4.5%2Bq%2A4.25\" \r\n" );
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document.write( "Solve this system:\r\n" );
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document.write( "\"system%284.5=p%2A4.25%2Bq%2A4%2C5=p%2A4.5%2Bq%2A4.25%29\" \r\n" );
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document.write( "Multiply both equations through by 100 to clear decimals\r\n" );
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document.write( "\"system%28450=p%2A425%2Bq%2A400%2C500=p%2A450%2Bq%2A425%29\"\r\n" );
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document.write( "Divide both equations through by 25\r\n" );
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document.write( "\"system%2818=p%2A17%2Bq%2A16%2C20=p%2A18%2Bq%2A17%29\"\r\n" );
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document.write( "\"system%2817p%2B16q=18%2C18p%2B17q=20%29\"\r\n" );
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document.write( "To eliminate p multiply first equation through by -18\r\n" );
document.write( "and second equation through by 17\r\n" );
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document.write( "\"system%28-306p-288q=-324%2C306p%2B289q=340%29\"\r\n" );
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document.write( "Add term by term\r\n" );
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document.write( "q = 16\r\n" );
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document.write( "Substitute 16 for q in\r\n" );
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document.write( "   17p+16q = 18\r\n" );
document.write( "17p+16(16) = 18\r\n" );
document.write( "   17p+256 = 18\r\n" );
document.write( "       17p = -238\r\n" );
document.write( "         p = -14\r\n" );
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document.write( "So the recursion formula is\r\n" );
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document.write( "an = -14an-1 + 16an-2, a(1)=4, a(2)=4.25, n=3,4,5,...\r\n" );
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document.write( "Edwin
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