document.write( "Question 1154147: There are
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Algebra.Com's Answer #776521 by ikleyn(52788) $\"\"$ $\"About$

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document.write( "Let x be the very central point for the given 4 terms of the AP.\r\n" );
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document.write( "In other words, let x be the average of the 4 terms of the AP\r\n" );
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document.write( "    x = .\r\n" );
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document.write( "Next, let d be the common difference of the AP.\r\n" );
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document.write( "Our goal is to find \"x\" and \"d\".\r\n" );
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document.write( "It is clear that \r\n" );
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document.write( "     = x - 1.5d;\r\n" );
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document.write( "     = x - 0.5d;\r\n" );
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document.write( "     = x + 0.5d;\r\n" );
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document.write( "     = x + 1.5d.\r\n" );
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document.write( "Therefore,   +  = 2x.\r\n" );
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document.write( "It implies  2x = 8, and hence  x = 4.\r\n" );
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document.write( "Also,   = 15.\r\n" );
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document.write( "It implies  (x-0.5d)*(x+0.5d) = 15,  or\r\n" );
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document.write( "            x^2 - 0.25d^2 = 15.\r\n" );
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document.write( "Substitute here x= 4 to get\r\n" );
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document.write( "            0.25d^2 = 4^2 - 15 = 16 - 15 = 1.\r\n" );
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document.write( "Thus  d^2 =  = 4;  hence,  d =  = +/- 2.\r\n" );
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document.write( "The problem is just solved. We know the central point x = 4  and the common difference d = +/-2.\r\n" );
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document.write( "If d = 2, then   = 4-1.5*2 = 1;   = 1+2 = 3;   = 3+2 = 5,  and   = 5 + 2 = 7.\r\n" );
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document.write( "If d = -2,  then we have the same sequence in the REVERSED order:   = 7;   = 5;   = 3  and   = 1.\r\n" );
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