document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=444308>Question 444308</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what is the nth term of: 3, 12, 27, 48, 75, 108...<BR>\n" );
document.write( "What is the nth term of: 3, 6, 11, 18, 27,38...<BR>\n" );
document.write( "What is the nth term of:4, 6.5, 9, 11.5, 14...<BR>\n" );
document.write( "what is the nth term of: 20, 17, 14, 11, 8...<BR>\n" );
document.write( " Please awnser fast. thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #306320 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=306320\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "1.\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;\" >\r<BR>\n" );
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document.write( "2.\r<BR>\n" );
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document.write( "The nth term is an equation to find any term using n the term you want to find.<BR>\n" );
document.write( "so, the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=nth ALIGN=MIDDLE  ALT=\"nth\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+term ALIGN=MIDDLE  ALT=\"+term\"   DISABLED_style= \"max-width:90%; height:auto;\" > for the sequence 2,3,4,5 is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2B1 ALIGN=MIDDLE  ALT=\"n%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "3.<BR>\n" );
document.write( "What is the nth term of:4, 6.5, 9, 11.5, 14...\r<BR>\n" );
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document.write( " the nth term is: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2%285n%2B3%29 ALIGN=MIDDLE  ALT=\"1%2F2%285n%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=1 ALIGN=MIDDLE  ALT=\"n=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%285%2A1%2B3%29=%281%2F2%29%288%29=4 ALIGN=MIDDLE  ALT=\"%281%2F2%29%285%2A1%2B3%29=%281%2F2%29%288%29=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=2 ALIGN=MIDDLE  ALT=\"n=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%285%2A12%2B3%29=%281%2F2%29%2813%29=6.5 ALIGN=MIDDLE  ALT=\"%281%2F2%29%285%2A12%2B3%29=%281%2F2%29%2813%29=6.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "4.<BR>\n" );
document.write( "the nth term is: \r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20+-+3%28n-1%29 ALIGN=MIDDLE  ALT=\"20+-+3%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "check:\r<BR>\n" );
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document.write( "20 - (n-1)3....n=1...20<BR>\n" );
document.write( "20 - (n-1)3....n=2...17\r<BR>\n" );
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document.write( "20 - (n-1)3....n=3...14\r<BR>\n" );
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document.write( " </SPAN>\n" );
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