document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1151010>Question 1151010</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the sum of 15 terms of an arithmetic series if the middle term is 92 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #772588 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</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=772588\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Consider the way that Gauss showed us how to sum an arithmetic sequence. \r<BR>\n" );
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document.write( "Your example is an arithmetic sequence so there is some number d that you add to each term to obtain the next term. \r<BR>\n" );
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document.write( "The middle term of a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15 ALIGN=MIDDLE  ALT=\"15\"   DISABLED_style= \"max-width:90%; height:auto;\" > term sequence is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=92 ALIGN=MIDDLE  ALT=\"92\"   DISABLED_style= \"max-width:90%; height:auto;\" >; so, this is the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" >th term. \r<BR>\n" );
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document.write( "The last term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" > terms further along in the sequence so it is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=92+%2B+7d ALIGN=MIDDLE  ALT=\"92+%2B+7d\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "Likewise the first term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" > terms before the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" >th term so it is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=92+-+7d ALIGN=MIDDLE  ALT=\"92+-+7d\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "Thus the sum of the first and last term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=92+-+7d+%2B+92+%2B+7d+=+92+%2B+92+=+184 ALIGN=MIDDLE  ALT=\"92+-+7d+%2B+92+%2B+7d+=+92+%2B+92+=+184\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "now use Gauss' technique to find the sum of the sequence\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=%28n%2F2%29%28a%5B1%5D%2Ba%5Bn%5D%29 ALIGN=MIDDLE  ALT=\"S=%28n%2F2%29%28a%5B1%5D%2Ba%5Bn%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" >=number of terms, <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;\" >=first term, 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;\" >=last term\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=%2815%2F2%29%28184%29 ALIGN=MIDDLE  ALT=\"S=%2815%2F2%29%28184%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=15%2A92 ALIGN=MIDDLE  ALT=\"S=15%2A92\"   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=1380 ALIGN=MIDDLE  ALT=\"S=1380\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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