document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=800964>Question 800964</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the first term of an arithmetic sequence is -14 while the sum of the first 20 term is 860. find the 20th term. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #483381 by </B><A HREF=/tutors/aboutme.mpl?userid=Finavon><B>Finavon(81)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Finavon><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=483381\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x = difference between terms and Sum(n) = sum of 1st n terms<BR>\n" );
document.write( "Series is -14, (-14+x), (-14+2x), (-14+3x), ... (-14+(n-1)*x)<BR>\n" );
document.write( "Sum(n) = -14 + (-14+x) + (-14+2x) + (-14+3x) + ... + (-14+(n-1)*x)<BR>\n" );
document.write( "Rearrange Sum(n) = (-14)*n + x*(1+2+3+ .. +(n-1))<BR>\n" );
document.write( "Add 2nd arithmetic series (reversed)<BR>\n" );
document.write( "Sum(n) = -14*n + x*( (1+2+3+ ..  +(n-1)) + ((n-1)+(n-2)+(n-3)+ .. +1) )/2<BR>\n" );
document.write( "=-14*n + x*n*(n-1)/2\r<BR>\n" );
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document.write( "So Sum(20)=-14*20+ x*20*(20-1)/2 = -280+x*20*19/2<BR>\n" );
document.write( "So 860=-280+190*x<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28860%2B280%29%2F190=1140%2F190=6+ ALIGN=MIDDLE  ALT=\"x=%28860%2B280%29%2F190=1140%2F190=6+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "20th term is -14+19*6=114-14=100<BR>\n" );
document.write( "20th term is 100 </SPAN>\n" );
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