document.write( "Question 1119641: Find three numbers in a geometric sequence where the third term is 4 times the first term and the difference between the second and the third term is 24. \n" ); document.write( "

Algebra.Com's Answer #735246 by ikleyn(52800) $\"\"$ $\"About$

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\n" ); document.write( "The problem has two solutions (two answers).\r
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\n" ); document.write( "\n" ); document.write( "One answer is the sequence 12, 24, 48, found by John.\r
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\n" ); document.write( "\n" ); document.write( "The second answer is the sequence 4, -8, 16.\r
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document.write( "The three terms are  a, ar and ar^2.\r\n" );
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document.write( "From the first part of the condition (\"the third term is 4 times the first term\") you have\r\n" );
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document.write( "ar^2 = 4a,\r\n" );
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document.write( "which implies  r^2 = 4  and, hence,  r = +/- 2.\r\n" );
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document.write( "1)  Let r = 2.  Then you get the sequence  12, 24, 48,  as John obtained it.\r\n" );
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document.write( "2)  Let r = -2.  \r\n" );
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document.write( "    Then the second part of the condition says\r\n" );
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document.write( "    ar^2 - ar = 24  ====>  a*4 - a*(-2) = 24  ====>  6a = 24  ====>  a = 4,\r\n" );
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document.write( "    and you get the second sequence  4, -8, 16.\r\n" );
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