document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1106829>Question 1106829</A>: <I><SPAN STYLE=\"word-break: break-all;\">  What is the next number in the sequence <BR>\n" );
document.write( "7, 21, 8, 72, 9  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #721812 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13198)</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=721812\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "It is NEVER possible, in ANY problem like this, to know the RIGHT answer.<br><BR>\n" );
document.write( "ANY next number would make a valid sequence.<br><BR>\n" );
document.write( "And any next number you find by a logical pattern might still be \"wrong\", because the author of the problem used a different logical pattern.<br><BR>\n" );
document.write( "Since it is never possible to know the right answer, it is never worthwhile to spend much time on any problem like this.  I usually spend no more than a minute or so, and if I can't see anything, I find better ways to spend my time and effort.<br><BR>\n" );
document.write( "In this one, I see the 7-8-9 as a separate sequence; then the other numbers are obtained from those:<BR>\n" );
document.write( "7*3 = 21<BR>\n" );
document.write( "8*9 = 8*3^2 = 72<BR>\n" );
document.write( "so 8*3^3 = 8^27 = 216<br><BR>\n" );
document.write( "But there is no way of knowing if this is the \"right\" answer.... </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );