document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1110479>Question 1110479</A>: <I><SPAN STYLE=\"word-break: break-all;\"> your sequence is as follows 1;5;14;30;55 and 8^th term is 204.\r<BR>\n" );
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document.write( "a)what type of sequence is this?<BR>\n" );
document.write( "b)find the nth formula </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #725479 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=725479\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1, 5, 14, 30, 55<BR>\n" );
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document.write( "This sequence is solved by using \"Level of Differences\" approach<BR>\n" );
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document.write( "Level 1 differences are 4, 9, 16, 25<BR>\n" );
document.write( "Level 2 differences are 5, 7, 9<BR>\n" );
document.write( "Level 3 differences are 2, 2<BR>\n" );
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document.write( "The Level 3 differences are the same, this tells us that the degree of the nth solution formula is 3<BR>\n" );
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document.write( "a)  the nth solution formula is a cubic equation<BR>\n" );
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document.write( "b)  the general form for a cubic solution formula for the nth term is<BR>\n" );
document.write( "An^3 + Bn^2 + Cn +D = nth term of sequence, where A, B, C, D are real numbers<BR>\n" );
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document.write( "We use the first 4 terms in the sequence<BR>\n" );
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document.write( "  A   +B  +C +D = 1<BR>\n" );
document.write( " 8A  +4B +2C +D = 5<BR>\n" );
document.write( "27A  +9B +3C +D = 14<BR>\n" );
document.write( "64A +16B +4C +D = 30<BR>\n" );
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document.write( "Now use your favorite solver for 4 linear equations in 4 unknowns<BR>\n" );
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document.write( "A = 1/3, B = 1/2, C = 1/6, D = 0<BR>\n" );
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document.write( "x(n) = n^3/3 +n^2/2 +n/6<BR>\n" );
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document.write( "we are given the 8th term is 204, so check with our formula<BR>\n" );
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document.write( "x(8) = (8^3/3) +(8^2/2) + 8/6<BR>\n" );
document.write( "x(8) = (512/3) +(64/2) +(8/6)<BR>\n" );
document.write( "x(8) = (1024/6) +(192/6) +(8/6)<BR>\n" );
document.write( "x(8) = 1224/6 = 204<BR>\n" );
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document.write( "the formula checks<BR>\n" );
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