Algebra.Com's Answer #846462 by ikleyn(52794)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "If 1st term of a GP is x and 3rd term is y, then\r\n" );
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document.write( " y =  , (1)\r\n" );
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document.write( "where r is the common ratio. If x is not zero, then we can divide both sides of this equation by x\r\n" );
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document.write( "  =  . (2)\r\n" );
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document.write( "Notice that in this case, when x =/= 0, from formula (1), both y and x have the same sign\r\n" );
document.write( "(both are either positive or negative), so the ratio is non-negative.\r\n" );
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document.write( "Hence, we can take square root of \r\n" );
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document.write( " r = +/-  ,\r\n" );
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document.write( "and in the case x =/= 0 it is the final answer to the problem's question, \r\n" );
document.write( "giving two possible values for r, if y =/= 0, or single zero, of y=0.\r\n" );
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document.write( "In the special case x=0 we CAN NOT divide by x (by zero), so formula (2) does not work.\r\n" );
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document.write( "In this case, the geometric progression is degenerated: all its terms are zeros.\r\n" );
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document.write( "So, the complete answer is r = +/- , if x =/= 0 (two possible values, if y =/= 0; or single 0, if y=0)\r\n" );
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document.write( " or any real number, if x = 0, but the GP in this case is degenerated and consists of zeros.\r\n" );
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document.write( "Solved completely with giving a complete answer.\r
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document.write( "This problem is, obviously, a trap.\r
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document.write( "The trap is that a COMPLETE answer is required, including the case x=0.\r
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