document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209803>Question 1209803</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let<BR>\n" );
document.write( "a + ar + ar^2 + ar^3 + \dotsb<BR>\n" );
document.write( "be an infinite geometric series. The sum of the series is 9. The sum of the cubes of all the terms is 36. Find the common ratio. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850647 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=850647\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bar%2Bar%5E2 ALIGN=MIDDLE  ALT=\"a%2Bar%2Bar%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >+...<br><BR>\n" );
document.write( "That sum is 9<br><BR>\n" );
document.write( "[1] <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2F%281-r%29=9 ALIGN=MIDDLE  ALT=\"a%2F%281-r%29=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E3%2Ba%5E3r%5E3%2Ba%5E3r%5E6 ALIGN=MIDDLE  ALT=\"a%5E3%2Ba%5E3r%5E3%2Ba%5E3r%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" >+...<br><BR>\n" );
document.write( "That sum is 36<br><BR>\n" );
document.write( "[2] <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E3%2F%281-r%5E3%29=36 ALIGN=MIDDLE  ALT=\"a%5E3%2F%281-r%5E3%29=36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "From [1],<br><BR>\n" );
document.write( "[3] <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E3=729%281-r%29%5E3 ALIGN=MIDDLE  ALT=\"a%5E3=729%281-r%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "From [2],<br><BR>\n" );
document.write( "[4] <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E3=36%281-r%5E3%29 ALIGN=MIDDLE  ALT=\"a%5E3=36%281-r%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Equating [3] and [4]...<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=729%281-r%29%5E3=36%281-r%5E3%29 ALIGN=MIDDLE  ALT=\"729%281-r%29%5E3=36%281-r%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281-r%5E3%29%2F%281-r%29%5E3=729%2F36=81%2F4 ALIGN=MIDDLE  ALT=\"%281-r%5E3%29%2F%281-r%29%5E3=729%2F36=81%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Simplify using <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-r%5E3=%281-r%29%281%2Br%2Br%5E2%29 ALIGN=MIDDLE  ALT=\"1-r%5E3=%281-r%29%281%2Br%2Br%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%281-r%29%281%2Br%2Br%5E2%29%29%2F%281-r%29%5E3=81%2F4 ALIGN=MIDDLE  ALT=\"%28%281-r%29%281%2Br%2Br%5E2%29%29%2F%281-r%29%5E3=81%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Br%2Br%5E2%29%2F%281-r%29%5E2=81%2F4 ALIGN=MIDDLE  ALT=\"%281%2Br%2Br%5E2%29%2F%281-r%29%5E2=81%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81%281-2r%2Br%5E2%29=4%281%2Br%2Br%5E2%29 ALIGN=MIDDLE  ALT=\"81%281-2r%2Br%5E2%29=4%281%2Br%2Br%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81-162r%2B81r%5E2=4%2B4r%2B4r%5E2 ALIGN=MIDDLE  ALT=\"81-162r%2B81r%5E2=4%2B4r%2B4r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=77r%5E2-166r%2B77=0 ALIGN=MIDDLE  ALT=\"77r%5E2-166r%2B77=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Use the quadratic formula to solve; choose the value of r that is less than 1, since both series converge.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=%28166-sqrt%28166%5E2-4%2877%29%2877%29%29%29%2F154 ALIGN=MIDDLE  ALT=\"r=%28166-sqrt%28166%5E2-4%2877%29%2877%29%29%29%2F154\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: r = 0.6755342 to several decimal places<br><BR>\n" );
document.write( " </SPAN>\n" );
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