document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=501418>Question 501418</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the first 12 terms of an arithmetic series is 186, and the 20th term is 83. What is the sum of the first 40 terms? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #338524 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20056)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=338524\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The sum of the first 12 terms of an arithmetic series is 186,<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B12%5D=expr%2812%2F2%29%282a%5B1%5D%2B%2812-1%29d%29 ALIGN=MIDDLE  ALT=\"S%5B12%5D=expr%2812%2F2%29%282a%5B1%5D%2B%2812-1%29d%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=186=6%282a%5B1%5D%2B11d%29 ALIGN=MIDDLE  ALT=\"186=6%282a%5B1%5D%2B11d%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=186%2F6=expr%286%2F6%29%282a%5B1%5D%2B11d%29 ALIGN=MIDDLE  ALT=\"186%2F6=expr%286%2F6%29%282a%5B1%5D%2B11d%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=31=1%282a%5B1%5D%2B11d%29 ALIGN=MIDDLE  ALT=\"31=1%282a%5B1%5D%2B11d%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=31=2a%5B1%5D%2B11d ALIGN=MIDDLE  ALT=\"31=2a%5B1%5D%2B11d\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%5B1%5D%2B11d=31 ALIGN=MIDDLE  ALT=\"2a%5B1%5D%2B11d=31\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r\n" );
document.write( "</PRE><BR>\n" );
document.write( "and the 20th term is 83. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=a%5B1%5D%2B%28n-1%29d ALIGN=MIDDLE  ALT=\"a%5Bn%5D=a%5B1%5D%2B%28n-1%29d\"   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=a%5B20%5D=a%5B1%5D%2B%2820-1%29d ALIGN=MIDDLE  ALT=\"a%5B20%5D=a%5B1%5D%2B%2820-1%29d\"   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=83=a%5B1%5D%2B19d ALIGN=MIDDLE  ALT=\"83=a%5B1%5D%2B19d\"   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=a%5B1%5D%2B19d=83 ALIGN=MIDDLE  ALT=\"a%5B1%5D%2B19d=83\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So we have this system:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%282a%5B1%5D%2B11d=31%2C+a%5B1%5D%2B19d=83%29 ALIGN=MIDDLE  ALT=\"system%282a%5B1%5D%2B11d=31%2C+a%5B1%5D%2B19d=83%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solve that system and get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D=-12 ALIGN=MIDDLE  ALT=\"a%5B1%5D=-12\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=5 ALIGN=MIDDLE  ALT=\"d=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "To get the sum of the first 40 terms:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B40%5D=expr%2840%2F2%29%282%28-12%29%2B%2840-1%295%29 ALIGN=MIDDLE  ALT=\"S%5B40%5D=expr%2840%2F2%29%282%28-12%29%2B%2840-1%295%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%5B40%5D=20%28-24%2B%2839%295%29 ALIGN=MIDDLE  ALT=\"S%5B40%5D=20%28-24%2B%2839%295%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Edwin</pre> </SPAN>\n" );
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