document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1108766>Question 1108766</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Consider the sequence where tn = 15 &#8722; 5n and the sum of the first m terms is &#8722;1250.<BR>\n" );
document.write( "Find the value of m. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #723770 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=723770\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The sum of the first m terms is m, multiplied by the average of all the terms.  In an arithmetic sequence, the average of all the terms is the average of the first and last terms.  So<BR>\n" );
document.write( "# terms = m<BR>\n" );
document.write( "1st term: 15-5(1) = 10<BR>\n" );
document.write( "m-th term: 15-5m<BR>\n" );
document.write( "<br><BR>\n" );
document.write( "The sum of first m terms is -1250:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%28%2810%2B%2815-5m%29%29%2F2%29+=+-1250 ALIGN=MIDDLE  ALT=\"m%28%2810%2B%2815-5m%29%29%2F2%29+=+-1250\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%2825-5m%29+=+-2500 ALIGN=MIDDLE  ALT=\"m%2825-5m%29+=+-2500\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25m-5m%5E2+=+-2500 ALIGN=MIDDLE  ALT=\"25m-5m%5E2+=+-2500\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5m%5E2-25m-2500+=+0 ALIGN=MIDDLE  ALT=\"5m%5E2-25m-2500+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5E2-5m-500+=+0 ALIGN=MIDDLE  ALT=\"m%5E2-5m-500+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28m-25%29%28m%2B20%29+=+0 ALIGN=MIDDLE  ALT=\"%28m-25%29%28m%2B20%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+25 ALIGN=MIDDLE  ALT=\"m+=+25\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+-20 ALIGN=MIDDLE  ALT=\"m+=+-20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Clearly only the positive solution to the equation makes sense in this problem.<br><BR>\n" );
document.write( "The number of terms in the sequence is 25. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );