document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1162437>Question 1162437</A>: <I><SPAN STYLE=\"word-break: break-all;\"> My co-worker got this exercise from somewhere regarding number sequences, and we can't figure it out.\r<BR>\n" );
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document.write( "6, 78, 85, 8, 17, 24, 10, 34, ??\r<BR>\n" );
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document.write( "We can't see a pattern and it feels like we've covered everything out there.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #786236 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=786236\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Don't spend too much time on any problem like this; it is IMPOSSIBLE to know the \"right\" answer.<br><BR>\n" );
document.write( "ANY next number will make a valid sequence.<br><BR>\n" );
document.write( "If a problem like this has an easily discernible answer, then there is a strong LIKELIHOOD that that answer is \"right\".<br><BR>\n" );
document.write( "But if there is no easily discernible pattern, there is no point in spending more than a minute (at most!) on the problem, since there is no way of knowing whether any answer you come up with is \"right\".<br><BR>\n" );
document.write( "I spent more time than I should have looking at the sequence while I was typing this response, and I see a possible pattern.<br><BR>\n" );
document.write( "The 6, 8, and 10 by themselves form a nice pattern.<br><BR>\n" );
document.write( "What is left after we account for those is three pairs of consecutive terms:<BR>\n" );
document.write( "78 and 85<BR>\n" );
document.write( "17 and 24<BR>\n" );
document.write( "34 and ??<br><BR>\n" );
document.write( "Since in the first two pairs the difference is 7, perhaps the difference in the last pair is also 7, making the missing number 41.<br><BR>\n" );
document.write( "But that is no more than a guess.........<br><BR>\n" );
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