document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=328501>Question 328501</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need to find the sum of the first n terms of the g.p. 4,12,36... and find the least value of n for which the sum is greater than 500,000.<BR>\n" );
document.write( "I know that <BR>\n" );
document.write( "r = 3 and a = 4 but then I am stuck. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #235309 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=235309\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the formula is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+a%2A%28%281-r%5E%28n%2B1%29%29%2F%281+-+r%29%29 ALIGN=MIDDLE  ALT=\"S+=+a%2A%28%281-r%5E%28n%2B1%29%29%2F%281+-+r%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+4 ALIGN=MIDDLE  ALT=\"a+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+3 ALIGN=MIDDLE  ALT=\"r+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+4%2A%28%281-3%5E%28n%2B1%29%29%2F%281+-+3%29%29 ALIGN=MIDDLE  ALT=\"S+=+4%2A%28%281-3%5E%28n%2B1%29%29%2F%281+-+3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+4%2A%28%281-3%5E%28n%2B1%29%29%2F%28-2%29%29 ALIGN=MIDDLE  ALT=\"S+=+4%2A%28%281-3%5E%28n%2B1%29%29%2F%28-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I'll find out when the sum is greater than 500000<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+4%2A%281-3%5E%28n%2B1%29%29%2F%28-2%29 ALIGN=MIDDLE  ALT=\"S+=+4%2A%281-3%5E%28n%2B1%29%29%2F%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+%28-2%29%2A%281-3%5E%28n%2B1%29%29 ALIGN=MIDDLE  ALT=\"S+=+%28-2%29%2A%281-3%5E%28n%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%2F%28-2%29+=+1+-+3%5E%28n%2B1%29 ALIGN=MIDDLE  ALT=\"S%2F%28-2%29+=+1+-+3%5E%28n%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%2F2+%2B+1+=+3%5E%28n%2B1%29 ALIGN=MIDDLE  ALT=\"S%2F2+%2B+1+=+3%5E%28n%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I can take the log of both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28S%2F2+%2B+1%29+=+%28n%2B1%29%2Alog%283%29 ALIGN=MIDDLE  ALT=\"log%28S%2F2+%2B+1%29+=+%28n%2B1%29%2Alog%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+50000 ALIGN=MIDDLE  ALT=\"S+=+50000\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the left side is close to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282.5%29+%2B+4 ALIGN=MIDDLE  ALT=\"log%282.5%29+%2B+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28log%282.5%29+%2B+4%29%2Flog%283%29+=+n+%2B+1 ALIGN=MIDDLE  ALT=\"%28log%282.5%29+%2B+4%29%2Flog%283%29+=+n+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+%28log%282.5%29+%2B+4%29%2Flog%283%29+-+1 ALIGN=MIDDLE  ALT=\"n+=+%28log%282.5%29+%2B+4%29%2Flog%283%29+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+4.39794%2F.477121+-+1 ALIGN=MIDDLE  ALT=\"n+=+4.39794%2F.477121+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+9.21766+-+1 ALIGN=MIDDLE  ALT=\"n+=+9.21766+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+8.21766 ALIGN=MIDDLE  ALT=\"n+=+8.21766\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Putting this back into formula,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+4%2A%28%281-3%5E%28n%2B1%29%29%2F%28-2%29%29 ALIGN=MIDDLE  ALT=\"S+=+4%2A%28%281-3%5E%28n%2B1%29%29%2F%28-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+4%2A%28%281-3%5E9.21766%29%2F%28-2%29%29 ALIGN=MIDDLE  ALT=\"S+=+4%2A%28%281-3%5E9.21766%29%2F%28-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+4%2A%281+-+25000.08621%29%2F%28-2%29 ALIGN=MIDDLE  ALT=\"S+=+4%2A%281+-+25000.08621%29%2F%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+-24999.08612%2A%28-2%29 ALIGN=MIDDLE  ALT=\"S+=+-24999.08612%2A%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+49998.17225 ALIGN=MIDDLE  ALT=\"S+=+49998.17225\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The next whole number for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I think that would put <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S ALIGN=MIDDLE  ALT=\"S\"   DISABLED_style= \"max-width:90%; height:auto;\" > over <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50000 ALIGN=MIDDLE  ALT=\"50000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" > seems to be too small </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );