document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=773298>Question 773298</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the terms of an infinite geometric sequence is 18 and the sum of the first two terms of the same sequence is 10. If some of the terms of the sequence are negative, what is the seventh term of the sequence?\r<BR>\n" );
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document.write( "Please help me answer this problem... Thanks a lot! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #471432 by </B><A HREF=/tutors/aboutme.mpl?userid=reviewermath><B>reviewermath(1029)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=reviewermath><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=reviewermath><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=471432\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Q:<BR>\n" );
document.write( "The sum of the terms of an infinite geometric sequence is 18 and the sum of the first two terms of the same sequence is 10. If some of the terms of the sequence are negative, what is the seventh term of the sequence? <BR>\n" );
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document.write( "A:<BR>\n" );
document.write( "S = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D%2F%281+-+r%29 ALIGN=MIDDLE  ALT=\"a%5B1%5D%2F%281+-+r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 18<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D ALIGN=MIDDLE  ALT=\"a%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 18(1 - r)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D ALIGN=MIDDLE  ALT=\"a%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5Dr ALIGN=MIDDLE  ALT=\"a%5B1%5Dr\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 10<BR>\n" );
document.write( "18(1 - r) + 18(1 - r)r = 10<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9r%5E2+-+4+=+0 ALIGN=MIDDLE  ALT=\"9r%5E2+-+4+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "r = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sqrt%284%2F9%29 ALIGN=MIDDLE  ALT=\"-sqrt%284%2F9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2F3 ALIGN=MIDDLE  ALT=\"-2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We choose the negative root because some terms are negative.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D ALIGN=MIDDLE  ALT=\"a%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%281+-+%28-2%2F3%29%29 ALIGN=MIDDLE  ALT=\"18%281+-+%28-2%2F3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 30<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B7%5D ALIGN=MIDDLE  ALT=\"a%5B7%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5Dr%5E6 ALIGN=MIDDLE  ALT=\"a%5B1%5Dr%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2830%29%28-2%2F3%29%5E6 ALIGN=MIDDLE  ALT=\"%2830%29%28-2%2F3%29%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28640%2F243%29 ALIGN=MIDDLE  ALT=\"highlight%28640%2F243%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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