Algebra.Com's Answer #740275 by ikleyn(52866)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "From the post, I hardly can read the small symbol \" t \" with subscript \" x \" and have no idea what does it mean.\r\n" );
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document.write( "But I guess, and my guessing is that  is the sum of the first 2 terms of some geometric progression, \r\n" );
document.write( "while  is the sum of the first 4 terms of the same geometric progression.\r\n" );
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document.write( "If so, then this info can be presented as these two equations\r\n" );
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document.write( "a + ar = 10, (1)\r\n" );
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document.write( "a + ar + ar^2 + ar^3 = 50 (2)\r\n" );
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document.write( "and the problem is to find the common ratio \"r\" from these equations.\r\n" );
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document.write( "We can rewrite equation (2) in the form\r\n" );
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document.write( "(a+ar) + r^2*(a+ar) = 50.\r\n" );
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document.write( "Replacing (a+ar) by 10 in this equation, based on (1), gives\r\n" );
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document.write( "10 + 10r^2 = 50,\r\n" );
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document.write( "which implies r^2 =  =  = 4 \r\n" );
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document.write( "and then r = +/-  = +/- 2.\r\n" );
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document.write( "Answer. The common ratio r may have two values: 2 or -2.\r\n" );
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document.write( "Solved.\r
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document.write( "Notice. It is possible to make one step further and to determine the first term \"a\" of the progression.\r
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document.write( " But since the problem does not ask to do it, I stop at this point.\r
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