document.write( "Question 529087: Consider the sequence x-3, x+1, 2x+8. One value for x is 5, making the sequence geometric.
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Algebra.Com's Answer #349492 by Edwin McCravy(20056) $\"\"$ $\"About$

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document.write( "The other tutor's solution is incorrect.\r\n" );
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document.write( "x-3, x+1, 2x+8\r\n" );
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document.write( "Let r = the common ratio \r\n" );
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document.write( "Then we have the system of two equations in two unknowns:\r\n" );
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document.write( "r(x-3) = x+1\r\n" );
document.write( "r(x+1) = 2x+8\r\n" );
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document.write( "Solving each for r:\r\n" );
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document.write( "r = \r\n" );
document.write( "r = \r\n" );
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document.write( "Setting the right sides equal to each other, since both\r\n" );
document.write( "equal to r:\r\n" );
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document.write( " = \r\n" );
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document.write( "Cross-multiplying:\r\n" );
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document.write( "(x+1)(x+1) = (x-3)(2x+8)\r\n" );
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document.write( "x² + 2x + 1 = 2x² + 2x - 24\r\n" );
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document.write( "0 = x² - 25\r\n" );
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document.write( "0 = (x - 5)(x + 5)\r\n" );
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document.write( " x - 5 = 0   x + 5 = 0\r\n" );
document.write( "     x = 5       x = -5\r\n" );
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document.write( "As they told us, x = 5 is one of the values and it\r\n" );
document.write( "makes the sequence\r\n" );
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document.write( "x-3, x+1, 2x+8 become\r\n" );
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document.write( "5-3, 5+1, 2(5)+8\r\n" );
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document.write( "2, 6, 18\r\n" );
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document.write( "and the common ratio is  =  = 3.\r\n" );
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document.write( "The other value of x is -5.  It makes the sequence\r\n" );
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document.write( "x-3, x+1, 2x+8 become:\r\n" );
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document.write( "-5-3, -5+1, 2(-5)+8\r\n" );
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document.write( "-8, -6, -2\r\n" );
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document.write( "and the ratio is  =  =   \r\n" );
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document.write( "Since the common ratio is less than 1, we can sum the series\r\n" );
document.write( "to infinity with the equation:\r\n" );
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document.write( " = \r\n" );
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document.write( "where  is the first term -8, and r = \r\n" );
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document.write( "Substituting:\r\n" );
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document.write( " =  =  =  = -12.\r\n" );
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document.write( "Edwin

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