document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1100724>Question 1100724</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the nth term for the sequence 3,12,27,48,75....<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #715251 by </B><A HREF=/tutors/aboutme.mpl?userid=richwmiller><B>richwmiller(17219)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richwmiller><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=richwmiller><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=715251\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> See #	Question 1100724 Answer by MathLover1\r<BR>\n" );
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document.write( "take the differences between the numbers to get:<BR>\n" );
document.write( "9, 15, 21, 27\r<BR>\n" );
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document.write( "take the second differences by taking the differences of the numbers above:<BR>\n" );
document.write( "6, 6, 6\r<BR>\n" );
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document.write( "all the second differences are equal to six, which means the equation is quadratic: y=ax^2+bx+c\r<BR>\n" );
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document.write( "we can find the a, b, & c values by pluggin in the points (1,3), (2,12), & (3,27) and solving for a,b,& c by elimination:\r<BR>\n" );
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document.write( "1a+1b+1c=3<BR>\n" );
document.write( "4a+2b+1c=12<BR>\n" );
document.write( "9a+3b+1c=27\r<BR>\n" );
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document.write( "1a+1b+1c=3<BR>\n" );
document.write( "3a+1b+0c=9<BR>\n" );
document.write( "8a+2b+0c=24\r<BR>\n" );
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document.write( "1a+1b+1c=3<BR>\n" );
document.write( "3a+1b+0c=9<BR>\n" );
document.write( "2a+0b+0c=6\r<BR>\n" );
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document.write( "2a=6<BR>\n" );
document.write( "a=3\r<BR>\n" );
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document.write( "3a+b=9<BR>\n" );
document.write( "b=0\r<BR>\n" );
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document.write( "a+b+c=3<BR>\n" );
document.write( "c=0\r<BR>\n" );
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document.write( "final equation of nth term is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3n%5E2%2B0n%2B0+=+3n%5E2 ALIGN=MIDDLE  ALT=\"3n%5E2%2B0n%2B0+=+3n%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3n%5E2 ALIGN=MIDDLE  ALT=\"+3n%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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