document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1184236>Question 1184236</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what should be the next number in this sequence:<BR>\n" );
document.write( " 4,14,14,1,5,2,1,9,3,___<BR>\n" );
document.write( "5,15,18,14,16,6,24,10,11,___ </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #814783 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=814783\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "There is no way to know the next number in either of these sequences, or in ANY problem where a sequence of numbers is given without any information about what type of sequence it is.<br><BR>\n" );
document.write( "In both of these sequences, ANY next number will make a valid sequence.<br><BR>\n" );
document.write( "Any problem like this must be considered a puzzle rather than a math problem.<br><BR>\n" );
document.write( "Presumably the author of this problem had logical patterns in mind when producing each of these sequences.  But in both of these cases (as in ANY similar problems) there are other logical patterns that produce the given numbers but produce different next numbers.<br><BR>\n" );
document.write( "Finally, it is absurd to simply look at the differences between successive terms in the 9 given numbers and say \"that's the pattern\".<br><BR>\n" );
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