document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1180708>Question 1180708</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Next number in this sequence:<BR>\n" );
document.write( "240, 234, 78, 72 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #810460 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=810460\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The other tutor is in fact right -- ANY next number will make a valid sequence.<br><BR>\n" );
document.write( "So this problem is a puzzle rather than a math problem that can be solved.<br><BR>\n" );
document.write( "However, you can get some good mental exercise by looking for patterns in the given numbers that suggest what A GOOD GUESS FOR THE NEXT NUMBER is.<br><BR>\n" );
document.write( "One pattern that should be easy to see is that 234 is 6 less than 240 and then 72 is 6 less than 78.<br><BR>\n" );
document.write( "So now look for a relationship between 234 and 78; it turns out that 78 is 234 divided by 3.<br><BR>\n" );
document.write( "So PERHAPS the given numbers follow the pattern \"subtract 6; divide by 3; repeat\".<br><BR>\n" );
document.write( "So a good guess for the next number is 72/3 = 24.<br><BR>\n" );
document.write( "But it is very possible that a very different pattern can be deduced from the given numbers that leads to a very different next number....<br><BR>\n" );
document.write( "So whenever you see a problem like this, take a little time (if you want to) to try to GUESS a logical next number; but realize it is never possible to know if any answer you come up with is \"right\".<br><BR>\n" );
document.write( "And the corollary to that is that nobody can tell you that any answer you come up with is wrong....<br><BR>\n" );
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document.write( "For thin-skinned tutor @ikleyn........<br><BR>\n" );
document.write( "Your response to this question about the posts from the other tutors shows very childish behavior.  It is NOT \"funny\" to watch such a thing from a grown woman.<br><BR>\n" );
document.write( "In my post, I said that you were right in saying that any number could be next.  I then went on to say that in any problem like this there is a possibility for getting some mental exercise for looking for a POSSIBLE logical answer.  I then went on to show that one POSSIBLE logical answer was 24.<br><BR>\n" );
document.write( "Then you laughed at me for \"PREDICTING\" that the next number was 24.<br><BR>\n" );
document.write( "I did no such thing.<br><BR>\n" );
document.write( "And the post from the other tutor showed a valid mathematical method for finding the next number in any problem like this by assuming the sequence is produced by a polynomial function of lowest possible degree.  Her post would have been better if it had stated that the method can be used to find a POSSIBLE next number.<br><BR>\n" );
document.write( "And you laughed at her response, even though it demonstrates a valid mathematical technique.<br><BR>\n" );
document.write( "Neither response was in any way an attempt to \"improve\" or \"disprove\" anything you wrote in your post.<br><BR>\n" );
document.write( "Stick to writing good responses to readers' questions and stop trying to make yourself look superior to other tutors.<br><BR>\n" );
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