document.write( "Question 1084079: Given that the first 5 terms of a geometric sequence are 3, x, 12, y, and 48, find, x and y. Assume both x and y are positive. \n" ); document.write( "

Algebra.Com's Answer #698154 by ikleyn(52835) $\"\"$ $\"About$

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document.write( "1.  Finding x.  \r\n" );
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document.write( "    You have these two equations\r\n" );
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document.write( "    x = 3*r,   (1)   where \"r\" is unknown common ratio\r\n" );
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document.write( "    12 = x*r.  (2)\r\n" );
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document.write( "    Substitute (1) into (2). You will get  12 = (3*r)*r   or   12 =.\r\n" );
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document.write( "    It implies  =  = 4.   Hence, r = 2 or -2.\r\n" );
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document.write( "    \r\n" );
document.write( "    It gives two solutions for x:  x = 3*2 = 6   and    x = 3*(-2) = -6.\r\n" );
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document.write( "2.  Finding y.\r\n" );
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document.write( "    You just found that there are two possibilities for the common ratio: r = 2  and  r = -2.\r\n" );
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document.write( "    At the first possibility,  y = 12^2 = 24.\r\n" );
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document.write( "    At the second possibility,  y = 12*(-2) = -24.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Answer. There are two solutions: (x,y): = (6,24) and (x,y) = (-6,-24).\r
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "On geometric progressions, read the introductory lessons\r
\n" ); document.write( "\n" ); document.write( "    - Geometric progressions\r
\n" ); document.write( "\n" ); document.write( "    - The proofs of the formulas for geometric progressions \r
\n" ); document.write( "\n" ); document.write( "    - Problems on geometric progressions\r
\n" ); document.write( "\n" ); document.write( "    - Word problems on geometric progressions\r
\n" ); document.write( "\n" ); document.write( "    - Solved problems on geometric progressions\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic \"Geometric progressions\".\r
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