document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1109379>Question 1109379</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Explicit formula the sequence & 12th term. \r<BR>\n" );
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document.write( "2, 6, 12, 20\r<BR>\n" );
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document.write( "Am I correct in having the formula be A(n)=n(n+1)? \r<BR>\n" );
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document.write( "This would make t he 12th term 156, right? \r<BR>\n" );
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document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #724359 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=724359\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2, 6, 12, 20<BR>\n" );
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document.write( "first level differences are<BR>\n" );
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document.write( "4, 6, 8<BR>\n" );
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document.write( "second level differences are<BR>\n" );
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document.write( "2, 2<BR>\n" );
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document.write( "therefore we know the formula is a quadratic of the form<BR>\n" );
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document.write( "an^2 +bn + c<BR>\n" );
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document.write( "for n=1, we have a +b +c = 2<BR>\n" );
document.write( "for n=2, we have 4a +2b +c = 6<BR>\n" );
document.write( "for n=3, we have 9a +3b +c = 12<BR>\n" );
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document.write( "we have a system of three equations in three unknowns<BR>\n" );
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document.write( "subtract the first equation from the second and third equations<BR>\n" );
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document.write( "3a +b = 4<BR>\n" );
document.write( "8a +2b = 10<BR>\n" );
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document.write( "using the first one, solve for b and substitute in the second one<BR>\n" );
document.write( "b = 4-3a<BR>\n" );
document.write( "8a +2(4-3a) = 10<BR>\n" );
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document.write( "8a +8 -6a = 10<BR>\n" );
document.write( "2a = 2<BR>\n" );
document.write( "a = 1<BR>\n" );
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document.write( "substitute for a in 3a +b = 4<BR>\n" );
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document.write( "3(1) + b = 4<BR>\n" );
document.write( "b = 1<BR>\n" );
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document.write( "a = 1 and b = 1, therefore<BR>\n" );
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document.write( "c = 0<BR>\n" );
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document.write( "our formula is n^2 +n<BR>\n" );
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document.write( "x(12) = 12^2 + 12 = 156<BR>\n" );
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document.write( "you are correct<BR>\n" );
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