document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=868395>Question 868395</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For the sequence 2, 9, 28, 65,... How do I find the next term and the rule for the nth term </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #523515 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=523515\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Subtract 1 from each term to get \r<BR>\n" );
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document.write( "2-1 = 1<BR>\n" );
document.write( "9-1 = 8<BR>\n" );
document.write( "28-1 = 27<BR>\n" );
document.write( "65-1 = 64\r<BR>\n" );
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document.write( "Each number on the right hand side (RHS) is a perfect cube\r<BR>\n" );
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document.write( "1 = 1^3<BR>\n" );
document.write( "8 = 2^3<BR>\n" );
document.write( "27 = 3^3<BR>\n" );
document.write( "64 = 4^3\r<BR>\n" );
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document.write( "So the rule is \"cube the number, then add 1\". We add 1 to undo the subtraction of 1 we did in the first part (see above)\r<BR>\n" );
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document.write( "So the rule is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28n%5E3+%2B+1%29 ALIGN=MIDDLE  ALT=\"highlight%28n%5E3+%2B+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where n is a positive whole number.\r<BR>\n" );
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document.write( "Once you get the general rule or formula, it's always a good idea to test it with the given sequence you already have. For instance, the third term is given to be 28. So if we did things right, then plugging n = 3 into the formula should give 28. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E3+%2B+1+=+3%5E3+%2B+1+=+27+%2B+1+=+28 ALIGN=MIDDLE  ALT=\"n%5E3+%2B+1+=+3%5E3+%2B+1+=+27+%2B+1+=+28\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this example confirms it. I recommend testing the other remaining terms.\r<BR>\n" );
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document.write( "The next term would be when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+5 ALIGN=MIDDLE  ALT=\"n+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so the next term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E3+%2B+1+=+5%5E3+%2B+1+=+125+%2B+1+=+highlight%28126%29 ALIGN=MIDDLE  ALT=\"n%5E3+%2B+1+=+5%5E3+%2B+1+=+125+%2B+1+=+highlight%28126%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Note: you can do each part in any order, but I find it easier to find the general rule/formula first. </SPAN>\n" );
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