document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1089737>Question 1089737</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi I would like know how to get the formula for this sequence 5;6;8;11;15  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #704090 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=704090\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 5;6;8;11;15 <BR>\n" );
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document.write( "we use the method of common differences<BR>\n" );
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document.write( "level 1 is 1, 2, 3, 4<BR>\n" );
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document.write( "level 2 is 1, 1, 1<BR>\n" );
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document.write( "therefore we know that we have a n^2 term<BR>\n" );
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document.write( "the general form is<BR>\n" );
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document.write( "an^2 + bn + c<BR>\n" );
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document.write( "we have the following<BR>\n" );
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document.write( "a(1^2) + b(1) +c = 5<BR>\n" );
document.write( "a(2^2) + b(2) +c = 6<BR>\n" );
document.write( "a(3^2) + b(3) +c = 8<BR>\n" );
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document.write( "so we have 3 equations in 3 unknowns<BR>\n" );
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document.write( " a +b  +c = 5<BR>\n" );
document.write( "4a +2b +c = 6<BR>\n" );
document.write( "9a +3b +c = 8<BR>\n" );
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document.write( "You can use whatever method you like, including using matrices in your graphing calculator<BR>\n" );
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document.write( "a = 1/2, b = -1/2, c = 5<BR>\n" );
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document.write( "the nth term is (n^2/2) -(n/2) + 5<BR>\n" );
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