document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1176684>Question 1176684</A>: <I><SPAN STYLE=\"word-break: break-all;\"> good day! have a series of numbers and i just want to know if this is a valid sequence.. thanks!\r<BR>\n" );
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document.write( "1<BR>\n" );
document.write( "3<BR>\n" );
document.write( "7<BR>\n" );
document.write( "8<BR>\n" );
document.write( "21<BR>\n" );
document.write( "49<BR>\n" );
document.write( "76<BR>\n" );
document.write( "224<BR>\n" );
document.write( "467<BR>\n" );
document.write( "514<BR>\n" );
document.write( "1155<BR>\n" );
document.write( "2683<BR>\n" );
document.write( "5216<BR>\n" );
document.write( "10544<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 #803902 by </B><A HREF=/tutors/aboutme.mpl?userid=Solver92311><B>Solver92311(821)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Solver92311><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=Solver92311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=803902\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "It is not an arithmetic sequence or a geometric sequence but a sequence is any list that follows a particular pattern. Since what you presented is a list that does follow a specific pattern, it is a sequence.  I have no idea what you mean by \"valid\" in this context.\r<BR>\n" );
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document.write( "What pattern?  When paired in one-to-one correspondence with any arithmetic sequence with equal cardinality, any finite list of numbers creates a set of ordered pairs that can be uniquely defined by a polynomial of degree one less than the cardinality of the original list.  Your sequence, which contains 14 elements, could be uniquely defined by a 13th-degree polynomial.\r<BR>\n" );
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document.write( "																<BR>\n" );
document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it.<BR>\n" );
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document.write( "From <https://www.algebra.com/cgi-bin/upload-illustration.mpl> <BR>\n" );
document.write( "I > Ø<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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