document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=116982>Question 116982</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395977258/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> This is a homework problem that I cannot seem to solve.  It states to:<BR>\n" );
document.write( "Find the sum of the first 20 terms of the series\r<BR>\n" );
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document.write( "1 + 8 + 64 + 512 + . . .\r<BR>\n" );
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document.write( "Can you please help?  Thank you in advance. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #85061 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=85061\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Notice that each term is increasing exponentially. So this sequence might be a geometric sequence. To find out, let's simply divide the terms.\r<BR>\n" );
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document.write( "First divide the 2nd term 8 by the 1st term 1 to get  \r<BR>\n" );
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document.write( "Now divide the 3rd term 64 by the 2nd term 8 to get  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64%2F8=8 ALIGN=MIDDLE  ALT=\"64%2F8=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Now divide the 4th term 512 by the 3rd term 64 to get  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=512%2F64=8 ALIGN=MIDDLE  ALT=\"512%2F64=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "So if we pick any term and divide it by the previous term, we'll always get . This is the common ratio between the terms. So this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=8 ALIGN=MIDDLE  ALT=\"r=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Now since we've started at 1, this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now remember, the formula for the sum of a geometric sequence is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%281-r%5En%29%2F%281-r%29 ALIGN=MIDDLE  ALT=\"a%281-r%5En%29%2F%281-r%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=1%281-8%5E20%29%2F%281-8%29 ALIGN=MIDDLE  ALT=\"1%281-8%5E20%29%2F%281-8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=1, r=8, and n=20  (since we want to find the sum of the first 20 terms)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281-8%5E20%29%2F%28-7%29 ALIGN=MIDDLE  ALT=\"%281-8%5E20%29%2F%28-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281-1.153%2A10%5E18%29%2F%28-7%29 ALIGN=MIDDLE  ALT=\"%281-1.153%2A10%5E18%29%2F%28-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Raise 8 to the 20th power to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.153%2A10%5E18 ALIGN=MIDDLE  ALT=\"1.153%2A10%5E18\"   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=%28-1.153%2A10%5E18%29%2F%28-7%29 ALIGN=MIDDLE  ALT=\"%28-1.153%2A10%5E18%29%2F%28-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.647%2A10%5E17 ALIGN=MIDDLE  ALT=\"1.647%2A10%5E17\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide\r<BR>\n" );
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document.write( "So the sum of the first 20 terms is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.647%2A10%5E17 ALIGN=MIDDLE  ALT=\"1.647%2A10%5E17\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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