document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=83996>Question 83996</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Is this correct?\r<BR>\n" );
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document.write( "Use the geometric sequence of numbers 1, 1/2, 1/4, 1/8,…to find the following:<BR>\n" );
document.write( "What is r, the ratio between 2 consecutive terms? \r<BR>\n" );
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document.write( "Answer:  r = (1/2)/1 = 1/2	<BR>\n" );
document.write( "Show work in this space.	\r<BR>\n" );
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document.write( "Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 10 terms? Please round your answer to 4 decimals.<BR>\n" );
document.write( "Answer: <BR>\n" );
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document.write( "S(n) = a(1)[r ^(n + 1) – 1)/(r – 1)<BR>\n" );
document.write( "S(10) = 1[(1/2) ^ 9 – 1] / [(1/2)-1]<BR>\n" );
document.write( "S(10) = [-0.998046875…] / [-0.5] = 1.99609375…\r<BR>\n" );
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document.write( "Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 12 terms? Please round your answer to 4 decimals.<BR>\n" );
document.write( "Answer:	<BR>\n" );
document.write( "Show work in this space. <BR>\n" );
document.write( "S(n) = a(1)[r ^(n + 1) – 1)/(r – 1)<BR>\n" );
document.write( "S(12) = 1[(1/2) ^ 9 – 1] / [(1/2)-1]<BR>\n" );
document.write( "S(12) = [-0.998046875…] / [-0.5] = 1.99609375…<BR>\n" );
document.write( "n = 12<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 #60446 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=60446\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "The ratio r is the factor to get from term to term. So <BR>\n" );
document.write( "r=nth term/(n-1) term<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=%281%2F8%29%2F%281%2F4%29=%284%2F8%29=1%2F2 ALIGN=MIDDLE  ALT=\"r=%281%2F8%29%2F%281%2F4%29=%284%2F8%29=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=1%2F2 ALIGN=MIDDLE  ALT=\"r=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The sequence is cut in half each term, so the sequence is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%5En ALIGN=MIDDLE  ALT=\"%281%2F2%29%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The sum of a geometric series is <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=a%281-r%5En%29%2F%281-r%29 ALIGN=MIDDLE  ALT=\"S=a%281-r%5En%29%2F%281-r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >where a=1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=%281-%281%2F2%29%5E10%29%2F%281-%281%2F2%29%29 ALIGN=MIDDLE  ALT=\"S=%281-%281%2F2%29%5E10%29%2F%281-%281%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >So plug in n=10 to find the sum of the first 10 partial sums<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=%281-1%2F1024%29%2F%281%2F2%29 ALIGN=MIDDLE  ALT=\"S=%281-1%2F1024%29%2F%281%2F2%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=2046%2F1024 ALIGN=MIDDLE  ALT=\"S=2046%2F1024\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the sum of the first ten terms is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2046%2F1024 ALIGN=MIDDLE  ALT=\"2046%2F1024\"   DISABLED_style= \"max-width:90%; height:auto;\" > or 1.99805 approximately\r<BR>\n" );
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document.write( "Use the same formula to find the sum of the 1st 12 terms <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=a%281-r%5En%29%2F%281-r%29 ALIGN=MIDDLE  ALT=\"S=a%281-r%5En%29%2F%281-r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >where a=1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=%281-%281%2F2%29%5E12%29%2F%281-%281%2F2%29%29 ALIGN=MIDDLE  ALT=\"S=%281-%281%2F2%29%5E12%29%2F%281-%281%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >So plug in n=12 to find the sum of the first 12 partial sums<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=%281-1%2F4096%29%2F%281%2F2%29 ALIGN=MIDDLE  ALT=\"S=%281-1%2F4096%29%2F%281%2F2%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=8190%2F4096 ALIGN=MIDDLE  ALT=\"S=8190%2F4096\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the sum of the first twelve terms is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8190%2F4096 ALIGN=MIDDLE  ALT=\"8190%2F4096\"   DISABLED_style= \"max-width:90%; height:auto;\" > or 1.99951 approximately\r<BR>\n" );
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