document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1156464>Question 1156464</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the general formula for the sequence: 0 1 4 10 20 35 56 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #779156 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=779156\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the difference between adjacent ones is 1/3/6/10/15/21. The next difference will be seven more from 21 or 28 and the term will ver 56+28, or 84.\r<BR>\n" );
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document.write( "The differences are<BR>\n" );
document.write( "0<BR>\n" );
document.write( "----1<BR>\n" );
document.write( "1-------2<BR>\n" );
document.write( "----3-------1\r<BR>\n" );
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document.write( "4-------3<BR>\n" );
document.write( "----6-------1\r<BR>\n" );
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document.write( "10------4<BR>\n" );
document.write( "----10------1<BR>\n" );
document.write( "20-----5<BR>\n" );
document.write( "----15-----1<BR>\n" );
document.write( "35-----6<BR>\n" );
document.write( "----21----1<BR>\n" );
document.write( "56\r<BR>\n" );
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document.write( "This will be a cubic polynomial, because the third differences are equal: an^3+bn^2+cn+d=0<BR>\n" );
document.write( "a=the third difference or 1<BR>\n" );
document.write( "12a+2b is first second difference or 2<BR>\n" );
document.write( "7a+3b+c=u2-u1 or 2-1 or 1<BR>\n" );
document.write( "and a+b+c+d= u1, which is 0\r<BR>\n" );
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document.write( "6a=1 so a =(1/6)<BR>\n" );
document.write( "12a+2b=2, and therefore 2b=0<BR>\n" );
document.write( "7a+3b+c=1 and therefore (7/6)-c=1 and c=-(1/6)<BR>\n" );
document.write( "a+b+c+d=0 and d will equal 0 as well.\r<BR>\n" );
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document.write( "The general formula is (1/6)n^3-(1/6)n<BR>\n" );
document.write( "don't factor it out.  For n=1 to 6, the numbers will be the sequence\r<BR>\n" );
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document.write( "when n=8 it will be (1/6)512-(8/6). that is (512-8)/6=84.\r<BR>\n" );
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document.write( "Sorry I was on autopilot.  Hope that helps.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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