document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=979757>Question 979757</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of 40 consecutive integers is 100. What is the smallest of these 40 integers? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #601011 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=601011\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 40 consecutive numbers add up to 100.  <BR>\n" );
document.write( "The numbers have to start less than 1.  The average is 2.5, so that is the middle of 40 integers.<BR>\n" );
document.write( "sum from -1 to -17 is -{n*(n+1)/2}=-153<BR>\n" );
document.write( "numbers 0,1,2 add up to 3.<BR>\n" );
document.write( "Integers greater than 2 add up to 250.<BR>\n" );
document.write( "Another way of saying that is that we want consecutive numbers from 1 that add up to 253,\r<BR>\n" );
document.write( "\n" );
document.write( "n*(n+1)/2=253;  n(n+1)=512<BR>\n" );
document.write( "n^2+n-506=0; (n+23)(n-22)=0; n=22, -23, positive root only.\r<BR>\n" );
document.write( "\n" );
document.write( "The number at the top are 22<BR>\n" );
document.write( "The number at the bottom is -17.<BR>\n" );
document.write( "Zero is the 40th number.<BR>\n" );
document.write( "The consecutive integers (40) are from -17 to 22.\r<BR>\n" );
document.write( "\n" );
document.write( "ANSWER: minus 17 is the smallest.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );