document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1188018>Question 1188018</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given that the first term and the common ratio of a geometric sequence are 3/8 and -2 respectively, and the sum of the first n terms is -8,191.875, find the sum of the (n+1) term to the (n+5) term. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #819067 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=819067\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "S(n) = a+ar+ar^2+...+ar^(n-1)<br><BR>\n" );
document.write( "S(n) = a(1+r+r^2+...+r^(n-1)<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%28n%29+=+a%28%281-r%5En%29%2F%281-r%29%29 ALIGN=MIDDLE  ALT=\"S%28n%29+=+a%28%281-r%5En%29%2F%281-r%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "We are given a=3/8, r=-2, and S(n) = -8191.875.  Plug the numbers into the formula to determine n.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8191.875+=+%283%2F8%29%28%281-%28-2%29%5En%29%2F%281-%28-2%29%29%29+=+%283%2F8%29%28%281-%28-2%29%5En%29%2F3%29+=+%281%2F8%29%28%281-%28-2%29%5En%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-%28-2%29%5En+=+8%28-8191.875%29=-65535 ALIGN=MIDDLE  ALT=\"1-%28-2%29%5En+=+8%28-8191.875%29=-65535\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28-2%29%5En+=+-65536+=+-2%5E16 ALIGN=MIDDLE  ALT=\"-%28-2%29%5En+=+-65536+=+-2%5E16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=16 ALIGN=MIDDLE  ALT=\"n=16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "We are to find the sum of the (n+1) term to the (n+5) term, or the sum of the 17th to 21st terms, which is S(21)-S(16).<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%2821%29+=+%281%2F8%29%28%281-%28-2%29%5E21%29%29+=+262144.125 ALIGN=MIDDLE  ALT=\"S%2821%29+=+%281%2F8%29%28%281-%28-2%29%5E21%29%29+=+262144.125\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "And then<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%2821%29-S%2816%29+=+262144.125-%28-8191.875%29+=+270336 ALIGN=MIDDLE  ALT=\"S%2821%29-S%2816%29+=+262144.125-%28-8191.875%29+=+270336\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: 270336<br><BR>\n" );
document.write( " </SPAN>\n" );
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