document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=817201>Question 817201</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The 2nd term of a geometric series is 80 and the sixth term is 16/125. Find the common ratio and the first term of the series. Find also the sum to infinity of the series.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #491934 by </B><A HREF=/tutors/aboutme.mpl?userid=Cromlix><B>Cromlix(4381)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Cromlix><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=Cromlix><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=491934\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Consider the series as starting with 80<BR>\n" );
document.write( "until you find the common ratio.<BR>\n" );
document.write( "a1 = 80, a5 = 16/125 and n = 5<BR>\n" );
document.write( "An = A2* r^5-1<BR>\n" );
document.write( "16/125 = 80* r^4<BR>\n" );
document.write( "Divide both sides by 80<BR>\n" );
document.write( "16/10000 = r^4<BR>\n" );
document.write( "Take the root 4 of 16/10000<BR>\n" );
document.write( "= 2/10<BR>\n" );
document.write( "= 1/5<BR>\n" );
document.write( "So the common ratio is 1/5<BR>\n" );
document.write( "Multiply 80 by 5<BR>\n" );
document.write( "First term = 400.<BR>\n" );
document.write( "....................<BR>\n" );
document.write( "Sum to Infinity = a/(1 - r)<BR>\n" );
document.write( "= 400/ (1 - 1/5)<BR>\n" );
document.write( "=400/ 4/5<BR>\n" );
document.write( "= 500<BR>\n" );
document.write( "Hope this helps.<BR>\n" );
document.write( ":-) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );