document.write( "Question 947874: Determine the x value on this sequence (16,35,x,91) and T1,T5and
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Algebra.Com's Answer #578690 by Edwin McCravy(20056)\"\" \"About 
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document.write( "y,z,16,35,x,91\r\n" );
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document.write( "Assume the general term is quadratic: \r\n" );
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document.write( "\"T%5Bn%5D=An%5E2%2BBn%2BC\" <--general term\r\n" );
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document.write( "Substituting n=3, T3=16\r\n" );
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document.write( "\"16=A%283%29%5E2%2BB%283%29%2BC\"\r\n" );
document.write( "\"16=9A%2B3B%2BC\"\r\n" );
document.write( "\"9A%2B3B%2BC=16\"\r\n" );
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document.write( "Substituting n=4, T2=35\r\n" );
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document.write( "\"35=A%284%29%5E2%2BB%284%29%2BC\"\r\n" );
document.write( "\"35=16A%2B4B%2BC\"\r\n" );
document.write( "\"16A%2B4B%2BC=35\"\r\n" );
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document.write( "Substituting n=6, T6=91\r\n" );
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document.write( "\"91=A%286%29%5E2%2BB%286%29%2BC\"\r\n" );
document.write( "\"91=36A%2B6B%2BC\"\r\n" );
document.write( "\"36A%2B6B%2BC=91\"\r\n" );
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document.write( "We have the system of equations:\r\n" );
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document.write( "\"system%289A%2B3B%2BC=16%2C16A%2B4B%2BC=35%2C36A%2B6B%2BC=91%29\"\r\n" );
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document.write( "Solve that system of equation and get\r\n" );
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document.write( "A=3, B=-2, C=-5\r\n" );
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document.write( "Substitute into our assumed general term:\r\n" );
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document.write( "\"T%5Bn%5D=An%5E2%2BBn%2BC\"\r\n" );
document.write( "\"T%5Bn%5D=3n%5E2-2n-5\"\r\n" );
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document.write( "\"x=T%5B5%5D\". Substituting n=5\r\n" );
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document.write( "\"x=T%5B5%5D=3%285%29%5E2-2%285%29-5\"\r\n" );
document.write( "\"x=T%5B5%5D=3%2825%29-10-5\"\r\n" );
document.write( "\"x=T%5B5%5D=75-15\"\r\n" );
document.write( "\"x=T%5B5%5D=60\"\r\n" );
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document.write( "\"y=T%5B1%5D\". Substituting n=1\r\n" );
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document.write( "\"y=T%5B1%5D=3%281%29%5E2-2%281%29-5\"\r\n" );
document.write( "\"y=T%5B1%5D=3%281%29-2-5\"\r\n" );
document.write( "\"y=T%5B5%5D=3-7\"\r\n" );
document.write( "\"y=T%5B5%5D=-4\"\r\n" );
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document.write( "\"z=T%5B2%5D\". Substituting n=1\r\n" );
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document.write( "\"z=T%5B2%5D=3%282%29%5E2-2%282%29-5\"\r\n" );
document.write( "\"z=T%5B2%5D=3%284%29-4-5\"\r\n" );
document.write( "\"z=T%5B5%5D=12-9\"\r\n" );
document.write( "\"z=T%5B5%5D=3\"\r\n" );
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document.write( "The sequence is -4,3,16,35,60,91,128,171,220,275,336,403,...\r\n" );
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document.write( "Edwin
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