document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1103432>Question 1103432</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Find the common ratio of a finite geometric series if the first term is 11, and the sum of the first 12 terms is 2922920. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #718160 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=718160\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "If the common ratio is r, then the sum of the first 12 terms is<BR>\n" );
document.write( "11+11r+11r^2+...+11r^11 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281-r%5E12%29%2F%281-r%29+=+2922920 ALIGN=MIDDLE  ALT=\"%281-r%5E12%29%2F%281-r%29+=+2922920\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "I don't know of an algebraic method for solving an equation like that.<BR>\n" );
document.write( "Graphing the left and right sides of the equation on a graphing calculator and looking for the intersection shows r=3.<br><BR>\n" );
document.write( "If we assume that the common ratio is a whole number, (almost a certainty, because the sum of the first 12 numbers is a whole number), then rough estimation of the 12th term can give us that answer:<BR>\n" );
document.write( "11*2^11 = 11*2048  too small<BR>\n" );
document.write( "11*4^11 = 11*2^22 = 11*2048^2  way too big </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );