document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=863255>Question 863255</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi I have a problem with formula for series. \r<BR>\n" );
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document.write( "The 1st 5 numbers are:  5, 10, 17, 26, 37. <BR>\n" );
document.write( "As you can see differences have differences themselves. I know the sequence would be quadratic because I worked it out: n^2+2n+2<BR>\n" );
document.write( "Next part of the question is how many blocks is it needed for 21 patterns. <BR>\n" );
document.write( "Formula for series with constant difference is there.  But the difference is changing so I don't know what to do, or what to google. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #520280 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=520280\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> quadratic series is n^2 + 2n + 2 as you discovered<BR>\n" );
document.write( "to find the sum of the first 21 patterns, we need to break this apart<BR>\n" );
document.write( "(sum)n^2 + (sum)2n + (sum)2, all from 1 to 21<BR>\n" );
document.write( "we know the sum for the power series n^2 is<BR>\n" );
document.write( "(n(n+1)(2n+1))/6<BR>\n" );
document.write( "the sum for 2n is the sum of even integers <BR>\n" );
document.write( "n(x1+xn)/2<BR>\n" );
document.write( "the sum of 21 \"2\"'s is<BR>\n" );
document.write( "21*2<BR>\n" );
document.write( "now we can put it all together<BR>\n" );
document.write( "(21*22*43)/6 + 21*(2+42)/2 + 42 = 3815<BR>\n" );
document.write( "you need 3815 blocks<BR>\n" );
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