document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1196058>Question 1196058</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the general rule/formula of the sequence: 7, 5, 3, ... </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #828758 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52810)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=828758\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
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document.write( "Another possible rule is to say that the given sequence lists 3 consecutive prime numbers in the descending order.\r<BR>\n" );
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document.write( "Then the expected next (and the last) term is 2.\r<BR>\n" );
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document.write( "Yet another possible formula is  &nbsp;&nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D ALIGN=MIDDLE  ALT=\"a%5Bn%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5+%2B+2%2Asin%28%28pi%2F2%29%2An%29 ALIGN=MIDDLE  ALT=\"5+%2B+2%2Asin%28%28pi%2F2%29%2An%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, &nbsp;&nbsp;n = 1, 2, 3, 4, 5, . . . \r<BR>\n" );
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document.write( "which gives the sequence repeating cyclically &nbsp;7, 5, 3, 5, 7, 5, 3, 5 . . . \r<BR>\n" );
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document.write( "Yet another formula is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D ALIGN=MIDDLE  ALT=\"a%5Bn%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 7 - 2*(n-1) + (n-1)*(n-2)*(n-3)*F(n),\r<BR>\n" );
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document.write( "where F(n) is an arbitrary polynomial with integer coefficients.\r<BR>\n" );
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document.write( "It produces the same three values at n = 1,2,3, but gives totally different values at n > 3.\r<BR>\n" );
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document.write( "I write it to explain you that more than one million possible \"rules\" and \"formulas\" can be created.\r<BR>\n" );
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document.write( "And without a context or additional info, you do not know and can not know, which is right and what to select.\r<BR>\n" );
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document.write( "So, mathematically, the problem and the question are quite non-sensical.\r<BR>\n" );
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document.write( "For a mathematically educated person, it is very important to understand it clearly.\r<BR>\n" );
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