document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1181525>Question 1181525</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the sum of the first term of an exponential sequence is 135 and the sum of the third and the fourth term is 60 given that the common ratio is positive calculate the limit of the sum of the first n^th term as n become large </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #811433 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=811433\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Presumably the first statement is supposed to be....<br><BR>\n" );
document.write( "the sum of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%28first%29 ALIGN=MIDDLE  ALT=\"cross%28first%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%28term%29 ALIGN=MIDDLE  ALT=\"cross%28term%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > first and second terms of an exponential sequence is 135.<br><BR>\n" );
document.write( "Then the problem has a \"nice\" solution.<br><BR>\n" );
document.write( "Let a and r be the first term and common ratio.  Then<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bar=135 ALIGN=MIDDLE  ALT=\"a%2Bar=135\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ar%5E2%2Bar%5E3+=+r%5E2%28a%2Bar%29+=+r%5E2%28135%29+=+60 ALIGN=MIDDLE  ALT=\"ar%5E2%2Bar%5E3+=+r%5E2%28a%2Bar%29+=+r%5E2%28135%29+=+60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2+=+60%2F135+=+4%2F9 ALIGN=MIDDLE  ALT=\"r%5E2+=+60%2F135+=+4%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Since we are told r is positive, r is 2/3.  Then<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bar+=+a%2B%282%2F3%29a+=+%285%2F3%29a+=+135 ALIGN=MIDDLE  ALT=\"a%2Bar+=+a%2B%282%2F3%29a+=+%285%2F3%29a+=+135\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+%283%2F5%29%28135%29+=+81 ALIGN=MIDDLE  ALT=\"a+=+%283%2F5%29%28135%29+=+81\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The infinite sum is first term divided by (1 minus the common ratio):<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2F%281-r%29+=+81%2F%281-2%2F3%29+=+81%2F%281%2F3%29+=+81%2A3+=+243 ALIGN=MIDDLE  ALT=\"a%2F%281-r%29+=+81%2F%281-2%2F3%29+=+81%2F%281%2F3%29+=+81%2A3+=+243\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: 243<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );