document.write( "Question 1135894: The ratio of the sum of the first three terms of a G.P to the sum of the first 6 terms is 27:19. The common ratio is
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Algebra.Com's Answer #753589 by ikleyn(52786)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "  \"a%5B1%5D\" + \"a%5B2%5D\" + \"a%5B3%5D\" + \"a%5B4%5D\" + \"a%5B5%5D\" + \"a%5B6%5D\" = \r\n" );
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document.write( "= \"a+%2B+ar+%2B+ar%5E2+%2B+ar%5E3+%2B+ar%5E4+%2B+ar%5E5\" = \"%28a+%2B+ar+%2B+ar%5E2%29\" + \"r%5E3%2A%28a%2Bar+%2B+ar%5E2%29\" = \"%281+%2B+r%5E3%29%2A%28a+%2B+ar+%2B+ar%5E2%29\".\r\n" );
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document.write( "Therefore,\r\n" );
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document.write( "\"%28a%2Bar+%2B+ar%5E2%29%2F%28a+%2B+ar+%2B+ar%5E2+%2B+ar%5E3+%2B+ar%5E4+%2B+ar%5E5%29\" = \"1%2F%281+%2B+r%5E3%29\" = \"27%2F19\".\r\n" );
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document.write( "Hence,   \"1+%2B+r%5E3\" = \"19%2F27\"   and  \"r%5E3\" = \"19%2F27+-+1\" = \"8%2F27\".\r\n" );
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document.write( "It implies   r = \"root%283%2C8%2F27%29\" = \"2%2F3\".\r\n" );
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document.write( "Answer.  r = \"2%2F3\",  which is the  first line of the option's list.\r\n" );
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