document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=984035>Question 984035</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the sixth term of a geometric series of positive number is 10 and the sixteenth term is 0.1. What is the eleventh term? Find its sum to infinity. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #604825 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=604825\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a sub n=a1 * r^n-1<BR>\n" );
document.write( "a6=10<BR>\n" );
document.write( "a16=0.1\r<BR>\n" );
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document.write( "Let a6 be the first term of the modified sequence.<BR>\n" );
document.write( "0.1=10*r^10<BR>\n" );
document.write( "10^-2=r^10=0.01<BR>\n" );
document.write( "r= 0.01^(1/10)=0.6309.  Without rounding.<BR>\n" );
document.write( "a1=100<BR>\n" );
document.write( "a11=1\r<BR>\n" );
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document.write( "Sum=a1 (1-r^n)/1-r<BR>\n" );
document.write( "=100*(.9)/1-r<BR>\n" );
document.write( "=90/(1-r); 1-r=0.3691(rounded)<BR>\n" );
document.write( "unrounded, answer is 243.87.\r<BR>\n" );
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document.write( "If one keeps the same ratio, which isn't quite 0.6, this works out exactly.  If one rounds to 0.6, it does not.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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