document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=83780>Question 83780</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I :<BR>\n" );
document.write( "Find the sum of the first 400 natural numbers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #60256 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=60256\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since the first 400 natural numbers is\r<BR>\n" );
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document.write( "1,2,3,4,5,6,7...399,400\r<BR>\n" );
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document.write( "The sequence is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=n ALIGN=MIDDLE  ALT=\"a%5Bn%5D=n\"   DISABLED_style= \"max-width:90%; height:auto;\" > where n starts at 1 and increments by 1\r<BR>\n" );
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document.write( "So to find the sum of the arithmetic sequence <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=n ALIGN=MIDDLE  ALT=\"a%5Bn%5D=n\"   DISABLED_style= \"max-width:90%; height:auto;\" > from 1 to 400 we can use this formula:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=n%28a%5B1%5D%2Ba%5Bn%5D%29%2F2 ALIGN=MIDDLE  ALT=\"S=n%28a%5B1%5D%2Ba%5Bn%5D%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > where S is the sum, n is the number of terms  (in this case 400), <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 (in this case 1), and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D ALIGN=MIDDLE  ALT=\"a%5Bn%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the last term (in this case 400)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=400%281%2B400%29%2F2 ALIGN=MIDDLE  ALT=\"S=400%281%2B400%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in n=400, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D=1 ALIGN=MIDDLE  ALT=\"a%5B1%5D=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=400 ALIGN=MIDDLE  ALT=\"a%5Bn%5D=400\"   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=400%28401%29%2F2 ALIGN=MIDDLE  ALT=\"S=400%28401%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=160400%2F2 ALIGN=MIDDLE  ALT=\"S=160400%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=80200 ALIGN=MIDDLE  ALT=\"S=80200\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide\r<BR>\n" );
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document.write( "So the sum of the first 400 natural numbers is 80,200 </SPAN>\n" );
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