document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1044698>Question 1044698</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the sum of the terms of a geometric sequence where the first term is 4, the last term is 324, and the common ratio is 3.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #660042 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=660042\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "To find the sum of a certain number of terms of a geometric sequence:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5Bn%5D=a%5B1%5D%281-r%5En%29%2F%281-r%29 ALIGN=MIDDLE  ALT=\"S%5Bn%5D=a%5B1%5D%281-r%5En%29%2F%281-r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5Bn%5D ALIGN=MIDDLE  ALT=\"S%5Bn%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >is the sum of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > terms (nth partial sum), <BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D ALIGN=MIDDLE  ALT=\"a%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the first term,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the common ratio.\r<BR>\n" );
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document.write( "if given the first term is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D=4 ALIGN=MIDDLE  ALT=\"a%5B1%5D=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the last term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=324 ALIGN=MIDDLE  ALT=\"a%5Bn%5D=324\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and the common ratio is <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;\" > than we need first to find what  number is the last term:\r<BR>\n" );
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document.write( "To find any term of a geometric sequence:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=a%5B1%5D%2Ar%5E%28n-1%29 ALIGN=MIDDLE  ALT=\"a%5Bn%5D=a%5B1%5D%2Ar%5E%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where a[1] is the first term of the sequence, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+ ALIGN=MIDDLE  ALT=\"r+\"   DISABLED_style= \"max-width:90%; height:auto;\" >is the common ratio, <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 the number of the term to find\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=324=4%2A3%5E%28n-1%29 ALIGN=MIDDLE  ALT=\"324=4%2A3%5E%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=324%2F4=3%5E%28n-1%29 ALIGN=MIDDLE  ALT=\"324%2F4=3%5E%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81=3%5E%28n-1%29 ALIGN=MIDDLE  ALT=\"81=3%5E%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E4=3%5E%28n-1%29 ALIGN=MIDDLE  ALT=\"3%5E4=3%5E%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........since base same, exponents must be same too, so we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4=n-1 ALIGN=MIDDLE  ALT=\"4=n-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=5 ALIGN=MIDDLE  ALT=\"n=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> so, your sequence have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > terms\r<BR>\n" );
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document.write( "than the sum will be:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B5%5D=4%281-3%5E5%29%2F%281-3%29 ALIGN=MIDDLE  ALT=\"S%5B5%5D=4%281-3%5E5%29%2F%281-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B5%5D=4%281-243%29%2F%28-2%29 ALIGN=MIDDLE  ALT=\"S%5B5%5D=4%281-243%29%2F%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B5%5D=2%28-242%29%2F%28-1%29 ALIGN=MIDDLE  ALT=\"S%5B5%5D=2%28-242%29%2F%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B5%5D=2%28242%29 ALIGN=MIDDLE  ALT=\"S%5B5%5D=2%28242%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B5%5D=484 ALIGN=MIDDLE  ALT=\"S%5B5%5D=484\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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