Algebra.Com's Answer #659647 by ikleyn(52788)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "if (x,y,12) is decreasing geometric sequence and (x,y,9) is arthemetic sequence then..evaluate the value of x,y and find Gn
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document.write( "1. Since (x,y,12) is a geometric sequence, you have\r\n" );
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document.write( "  =  , or  =  . (1)\r\n" );
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document.write( "2. Since (x,y,9) is an arithmetic sequence, you have\r\n" );
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document.write( " y - x = 9 - y, or 2y = 9 + x (2)\r\n" );
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document.write( "3. From (2), express x = 2y-9 and substitute it into (1). You will get\r\n" );
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document.write( " = 12*(2y-9), or\r\n" );
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document.write( "  =  .\r\n" );
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document.write( " The solutions are y = 6 and/or 18.\r\n" );
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document.write( "4. a) If y = 6, then the first progression (GP) is (3, 6, 12) and the second progression (AP) is (3, 6, 9).\r\n" );
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document.write( " b) If y = 18, then the first progression (GP) is (27, 18, 12) and the second progression (AP) is (27, 18, 9).\r\n" );
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document.write( "5. Since the GP is decreasing, it leaves only one answer: b)\r\n" );
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document.write( "These two lessons in this site\r
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document.write( " - One characteristic property of arithmetic progressions\r
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document.write( " - One characteristic property of geometric progressions\r
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document.write( "helped me to quickly solve the problem.\r
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