document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1170436>Question 1170436</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the 5th term in a geometric progression is 9 times the 3rd term and the sum of the 6th and 7th terms is 1944. determine the common ratio, the first term the sum of the 4th to 10th terms inclusive<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #795330 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=795330\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the common ratio is 3 since between the 3rd and 5th is a 9-fold increase<BR>\n" );
document.write( "a1 is unknown<BR>\n" );
document.write( "a2=3a1<BR>\n" );
document.write( "a3=9a1<BR>\n" );
document.write( "a5=81a1<BR>\n" );
document.write( "a6=243a1<BR>\n" );
document.write( "a7=729a1<BR>\n" );
document.write( "the last two add to 1944=972a1<BR>\n" );
document.write( "so a1=2, and r=3<BR>\n" );
document.write( "-<BR>\n" );
document.write( "sum of first 10 terms is 2(1-3^10)/-2=59048<BR>\n" );
document.write( "sum of first four terms is 2(1-3^4)/-2=80<BR>\n" );
document.write( "the sum of the 4th-10th terms inclusive is 58968<BR>\n" );
document.write( "the series is 2/6/18/54/162/486/1458/4374/13122/39366<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );