document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=15836>Question 15836</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have a set of ordered pairs and I can see the pattern but I can't figure out the formula that relates them.  This was a challenge question in my pre-algebra class.<BR>\n" );
document.write( "(1,1) (2,3) (3,6) (4,10) (5,15)....  I graphed it but I don't know yet how that helps me.  Thanks -Iris </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #8041 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=8041\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This was a challenge question in my pre-algebra class.<BR>\n" );
document.write( "(1,1) (2,3) (3,6) (4,10) (5,15).... <BR>\n" );
document.write( " key to such problems is to analyse the pattern...each is an ordered pair <BR>\n" );
document.write( "   1st numbers in the ordered pairs are 1,2,3,4,5..etc...so each increases by 1 so graph these seperately if you want .you will find a straight line ..here     n th. number is n if we call these as x1,x2,x3,x4,x5...etc then xn=n ...( you can check by putting n=1,2,3 etc when you will get the first numbers in the pairs as 1,2,3,4,5..etc.. ) <BR>\n" );
document.write( "now 2nd nos. are 1,3,6,10,15..no constant difference or ratio is visible so try the differences between pairs of consecutive numbers..<BR>\n" );
document.write( "  3-1=2<BR>\n" );
document.write( "  6-3 =3<BR>\n" );
document.write( "10-6=4<BR>\n" );
document.write( "15-10=5...now this is a pattern ..if we call the                                1 = y1...3=y2...6=y3...10=y4...15=y5..then <BR>\n" );
document.write( "  y2-y1=2<BR>\n" );
document.write( "y3-y2=3<BR>\n" );
document.write( "y4-y3=4<BR>\n" );
document.write( "y5-y4=5<BR>\n" );
document.write( "....<BR>\n" );
document.write( "....<BR>\n" );
document.write( "yn-y(n-1)= n...see the pattern ..check if you want as explained above <BR>\n" );
document.write( " <BR>\n" );
document.write( "add all the above ...we get <BR>\n" );
document.write( " yn-y1=2+3+4+5+...n <BR>\n" );
document.write( " yn = y1+2+3+4+5+......n =1+2+3+4+5+.....n =you will learn it as equal to          n(n+1)/2 <BR>\n" );
document.write( " hence yn =n(n+1)/2 ....check if you want as explained above <BR>\n" );
document.write( " that is put n=1,2,3,4,5...etc in n(n+1)/2.. ...we get..y1,y2,y3,y4,y5...etc.as 1,3,6,10,15...respectively\r<BR>\n" );
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