document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1163035>Question 1163035</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum to infinity of a GP is twice the sum of the first two terms.<BR>\n" );
document.write( "Find possible values of 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 #786984 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</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=786984\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "With first term a and common ratio r....<br><BR>\n" );
document.write( "the sum of the first two terms is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bar ALIGN=MIDDLE  ALT=\"a%2Bar\"   DISABLED_style= \"max-width:90%; height:auto;\" >;<BR>\n" );
document.write( "the infinite sum is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2F%281-r%29 ALIGN=MIDDLE  ALT=\"a%2F%281-r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The condition is that the infinite sum be twice the sum of the first two terms:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2F%281-r%29+=+2%28a%2Bar%29 ALIGN=MIDDLE  ALT=\"a%2F%281-r%29+=+2%28a%2Bar%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%281-r%29+=+2%281%2Br%29 ALIGN=MIDDLE  ALT=\"1%2F%281-r%29+=+2%281%2Br%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2+=+1-r%5E2 ALIGN=MIDDLE  ALT=\"1%2F2+=+1-r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2+=+1%2F2 ALIGN=MIDDLE  ALT=\"r%5E2+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+sqrt%282%29%2F2 ALIGN=MIDDLE  ALT=\"r+=+sqrt%282%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+-sqrt%282%29%2F2 ALIGN=MIDDLE  ALT=\"r+=+-sqrt%282%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Both solutions satisfy the condition of the problem.<br><BR>\n" );
document.write( "ANSWER: The possible common ratios are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29%2F2 ALIGN=MIDDLE  ALT=\"sqrt%282%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sqrt%282%29%2F2 ALIGN=MIDDLE  ALT=\"-sqrt%282%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );