document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=210252>Question 210252</A>: <I><SPAN STYLE=\"word-break: break-all;\"> make a conjecture in terms of Q(n)(find the nth term) for the following sequence & then find the 100th term:n= 1  2  3    4  5   6 <BR>\n" );
document.write( "                                    Q= 3 12  25  42  63  88\r<BR>\n" );
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document.write( "Cannot figure out any part of this...I would really appreciate any help at this point!<BR>\n" );
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 #158884 by </B><A HREF=/tutors/aboutme.mpl?userid=scott8148><B>scott8148(6628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=scott8148><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=scott8148><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=158884\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the differences between consecutive Q terms are ___ 9, 13, 17, 21, 25\r<BR>\n" );
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document.write( "the difference between consecutive terms of the 1st set of differences is equal to 4 and is constant<BR>\n" );
document.write( "___ this means that the conjecture is a second order expression (2nd differences constant)\r<BR>\n" );
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document.write( "Q(n) = an^2 + bn + c\r<BR>\n" );
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document.write( "Q(1) = a(1^2) + b(1) + c ___ 3 = a + b + c ___ 3 - a - b = c\r<BR>\n" );
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document.write( "Q(2) = a(2^2) + b(2) + c ___ 12 = 4a + 2b + c<BR>\n" );
document.write( "substituting ___ 12 = 4a + 2b + 3 - a - b ___ 9 = 3a + b\r<BR>\n" );
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document.write( "Q(3) = a(3^2) + b(3) + c ___ 25 = 9a + 3b + c<BR>\n" );
document.write( "substituting ___ 25 = 9a + 3b + 3 - a - b ___ 22 = 8a + 2b ___ 11 = 4a + b\r<BR>\n" );
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document.write( "subtracting equations ___ 2 = a\r<BR>\n" );
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document.write( "substituting ___ 11 = 4(2) + b ___ 3 = b\r<BR>\n" );
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document.write( "substituting ___ 3 - 2 - 3 = c ___ -2 = c\r<BR>\n" );
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document.write( "Q(n) = 2n^2 + 3n - 2\r<BR>\n" );
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document.write( "Q(100) = 2(100^2) + 3(100) - 2 = 20298 </SPAN>\n" );
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