<PRE><B>Question 1180708</B>
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The other tutor is in fact right -- ANY next number will make a valid sequence.&lt;br&gt;
So this problem is a puzzle rather than a math problem that can be solved.&lt;br&gt;
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.&lt;br&gt;
One pattern that should be easy to see is that 234 is 6 less than 240 and then 72 is 6 less than 78.&lt;br&gt;
So now look for a relationship between 234 and 78; it turns out that 78 is 234 divided by 3.&lt;br&gt;
So PERHAPS the given numbers follow the pattern &quot;subtract 6; divide by 3; repeat&quot;.&lt;br&gt;
So a good guess for the next number is 72/3 = 24.&lt;br&gt;
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....&lt;br&gt;
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 &quot;right&quot;.&lt;br&gt;
And the corollary to that is that nobody can tell you that any answer you come up with is wrong....&lt;br&gt;
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For thin-skinned tutor @ikleyn........&lt;br&gt;
Your response to this question about the posts from the other tutors shows very childish behavior.  It is NOT &quot;funny&quot; to watch such a thing from a grown woman.&lt;br&gt;
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.&lt;br&gt;
Then you laughed at me for &quot;PREDICTING&quot; that the next number was 24.&lt;br&gt;
I did no such thing.&lt;br&gt;
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.&lt;br&gt;
And you laughed at her response, even though it demonstrates a valid mathematical technique.&lt;br&gt;
Neither response was in any way an attempt to &quot;improve&quot; or &quot;disprove&quot; anything you wrote in your post.&lt;br&gt;
Stick to writing good responses to readers&#39; questions and stop trying to make yourself look superior to other tutors.&lt;br&gt;
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