document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1037774>Question 1037774</A>: <I><SPAN STYLE=\"word-break: break-all;\"> First question:<BR>\n" );
document.write( "A geometric sequence consisting of four terms in which ratio is positive, the sum of the first two terms is 8 and the sum of the last two terms is 72. Find the sequence\r<BR>\n" );
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document.write( "Second question:<BR>\n" );
document.write( "Find three numbers in a geometric sequence whose sum is 42 and whose product is 512 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #652586 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=652586\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For the first question:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%5B1%5D%2Bg%5B2%5D+=+8 ALIGN=MIDDLE  ALT=\"g%5B1%5D%2Bg%5B2%5D+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%5B3%5D%2Bg%5B4%5D+=+72 ALIGN=MIDDLE  ALT=\"g%5B3%5D%2Bg%5B4%5D+=+72\"   DISABLED_style= \"max-width:90%; height:auto;\" > ==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%5B1%5D%2Bg%5B1%5D%2Ar+=+g%5B1%5D%2A%281%2Br%29+=+8 ALIGN=MIDDLE  ALT=\"g%5B1%5D%2Bg%5B1%5D%2Ar+=+g%5B1%5D%2A%281%2Br%29+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%5B3%5D%2Bg%5B4%5D+=+g%5B1%5D%2Ar%5E2+%2B+g%5B1%5D%2Ar%5E3+=+g%5B1%5D%2Ar%5E2%281%2Br%29+=+72 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Dividing the second equation by the first equation, we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2+=+9 ALIGN=MIDDLE  ALT=\"r%5E2+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which means r = 3.  (r = -3 is not acceptable, as the ratio should be positive.)\r<BR>\n" );
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document.write( "The sequence is thus 2, 6, 18, 54.\r<BR>\n" );
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document.write( "For the second question:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%5B1%5D%2Bg%5B1%5D%2Ar+%2B+g%5B1%5D%2Ar%5E2+=+42+ ALIGN=MIDDLE  ALT=\"g%5B1%5D%2Bg%5B1%5D%2Ar+%2B+g%5B1%5D%2Ar%5E2+=+42+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%5B1%5D%2Ag%5B1%5Dr%2Ag%5B1%5Dr%5E2+=+512 ALIGN=MIDDLE  ALT=\"g%5B1%5D%2Ag%5B1%5Dr%2Ag%5B1%5Dr%5E2+=+512\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The second equation gives <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28g%5B1%5D%2Ar%29%5E3+=+512 ALIGN=MIDDLE  ALT=\"%28g%5B1%5D%2Ar%29%5E3+=+512\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which implies that  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%5B1%5D%2Ar+=+8 ALIGN=MIDDLE  ALT=\"g%5B1%5D%2Ar+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, after taking cube roots of both sides.\r<BR>\n" );
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document.write( "The first equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%5B1%5D%2Bg%5B1%5D%2Ar+%2B+g%5B1%5D%2Ar%5E2+=+42+ ALIGN=MIDDLE  ALT=\"g%5B1%5D%2Bg%5B1%5D%2Ar+%2B+g%5B1%5D%2Ar%5E2+=+42+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equivalent to <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%5B1%5D%2A%281%2Br%2Br%5E2%29+=+42 ALIGN=MIDDLE  ALT=\"g%5B1%5D%2A%281%2Br%2Br%5E2%29+=+42\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Dividing this equation with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%5B1%5D%2Ar+=+8 ALIGN=MIDDLE  ALT=\"g%5B1%5D%2Ar+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Br%2Br%5E2%29%2Fr+=+21%2F4 ALIGN=MIDDLE  ALT=\"%281%2Br%2Br%5E2%29%2Fr+=+21%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4r%5E2%2B4r%2B4+=+21r ALIGN=MIDDLE  ALT=\"4r%5E2%2B4r%2B4+=+21r\"   DISABLED_style= \"max-width:90%; height:auto;\" > <==>  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4r%5E2+-+17r%2B4+=+0 ALIGN=MIDDLE  ALT=\"4r%5E2+-+17r%2B4+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > <==> r = 1/4 or 4.\r<BR>\n" );
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document.write( "If r = 1/4, the sequence is 32, 8, 2.<BR>\n" );
document.write( "If r = 4, the sequence is 2, 8, 32. </SPAN>\n" );
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