document.write( "Question 1208816: If the 3rd term of a gp is four times its 5th term, find the possible values of the common ratio \n" ); document.write( "

Algebra.Com's Answer #847279 by ikleyn(52788) $\"\"$ $\"About$

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document.write( "If the 3rd term of a gp is four times its 5th term, we can write this equation\r\n" );
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document.write( "     = ,    (valid for any GP)\r\n" );
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document.write( "     = .     (because the 3rd term of the GP is four times its 5th term).\r\n" );
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document.write( "It implies\r\n" );
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document.write( "     =  = .\r\n" );
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document.write( "If   =/= 0,  then from previous equation we have\r\n" );
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document.write( "    4*r^2 = 1,  r^2 = ,\r\n" );
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document.write( "which has two solutions  r =  = +/- .\r\n" );
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document.write( "ANSWER.   In regular case, when the GP is not zero-sequence,  the common ratio is either    or  .\r\n" );
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document.write( "          If case of zero-sequence, the common ratio can be any real number.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "Thanks to @greenestamps for noticing my error in previous version.\r
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\n" ); document.write( "\n" ); document.write( "Now you see the corrected solution.\r
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