document.write( "Question 1205956: The third term of a g.p is 12 and the first term is 48.find the sum of the first 11 terms \n" ); document.write( "
Algebra.Com's Answer #843084 by ikleyn(52790)\"\" \"About 
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\n" ); document.write( "The third term of a g.p is 12 and the first term is 48. find the sum of the first 11 terms
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\n" ); document.write( "\n" ); document.write( "        This problem allows two solutions :   there are two  GPs  satisfying the given condition,
\n" ); document.write( "        and they produce two different sums,  i.e. two different answers.\r
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\n" ); document.write( "\n" ); document.write( "        Thus the solution by @mananth is  INCOMPLETE  and,  therefore,  partly  INCORRECT.\r
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\n" ); document.write( "\n" ); document.write( "        I came to bring a correct solution.\r
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document.write( "For the third term of this GP, we have this equation\r\n" );
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document.write( "    12 = 48*r^2.\r\n" );
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document.write( "It gives\r\n" );
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document.write( "    r^2 = \"12%2F48\" = \"1%2F4\",\r\n" );
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document.write( "    r = \"sqrt%281%2F4%29\" = +/- \"1%2F2\".\r\n" );
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document.write( "So, there are two values for common ratio: one is  r = 1/2; the other is r = -1/2.\r\n" );
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document.write( "With common ratio 1/2, the sum of the first 11 terms of the GP is \r\n" );
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document.write( "    \"S%5B11%5D\" = \"48%2A%281+-+%281%2F2%29%5E11%29%2F%281-1%2F2%29\" = \"48%2A%28%282%5E11-1%29%2F2%5E11%29%2F%28%281%2F2%29%29\" = \"48%2A2%2A%28%282%5E11-1%29%2F2%5E11%29\" = \"3%2A%282047%2F64%29\" = 95.953125  (rounded)\r\n" );
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document.write( "With common ratio -1/2, the sum of the first 11 terms of the GP is \r\n" );
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document.write( "    \"S%5B11%5D\" = \"48%2A%281+%2B+%281%2F2%29%5E11%29%2F%281%2B1%2F2%29\" = \"48%2A%28%282%5E11%2B1%29%2F2%5E11%29%2F%28%283%2F2%29%29\" = \"48%2A2%2A%282%5E11%2B1%29%2F%283%2A2%5E11%29\" = \"32%2A%282049%2F2%5E11%29\" = \"2049%2F64\" = 32.015625  (rounded).\r\n" );
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document.write( "ANSWER. Two possible answers are  \"3%2A%282047%2F64%29\" = 95.953125 (with r = 1/2)  and  \"2049%2F64\" = 32.015625  (with r = -1/2).\r\n" );
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