document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1034674>Question 1034674</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what is the sum of the first  100 natural Numbers excluding the multiples if 4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #649330 by </B><A HREF=/tutors/aboutme.mpl?userid=sachi><B>sachi(548)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=sachi><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=sachi><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=649330\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the sum first  100 natural Numbers i.e 1+2+3+.....+100<BR>\n" );
document.write( "as per AP<BR>\n" );
document.write( "the first term=1=a<BR>\n" );
document.write( "the common diff =1-d<BR>\n" );
document.write( "no of terms   = 100=n<BR>\n" );
document.write( "now the sum=n/2[2a+(n-1)*d)=100*101/2=5050<BR>\n" );
document.write( "now the sum of multiples of 4=4+8+12+.....+100<BR>\n" );
document.write( "the last term=100=l<BR>\n" );
document.write( "the first term=4=a<BR>\n" );
document.write( "the common diff =4-d<BR>\n" );
document.write( "no of terms=n<BR>\n" );
document.write( "then 100=a+(n-1)*d=4+(n-1)*4=4n<BR>\n" );
document.write( "so n=25\r<BR>\n" );
document.write( "\n" );
document.write( "now the sum of multiples of 4=4+8+12+.....+100=25/2(a+l)=25/2*(4+100)=1300<BR>\n" );
document.write( "so the sum of the first  100 natural Numbers excluding the multiples if 4<BR>\n" );
document.write( "=5050-1300=3750 <BR>\n" );
document.write( "ans </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );