Question 1180708: Next number in this sequence:
240, 234, 78, 72
Found 3 solutions by ikleyn, greenestamps, MathLover1:
Answer by ikleyn(52786)   (Show Source):
You can put this solution on YOUR website! .
Any number can be next.
For example, 12, -73, 179.347, -84,  ,  or  , or any other number.
The posed question is mathematically nonsensical.
Have a nice day (!)
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Of the two tutors, who came after me to "disprove" or "improve" my answer,
one predicts next number as 24, while the other predicts it as 516.
It is very funny to watch their efforts, that only strengthen the validity of my answer.
Really, it deserves to be posted to New York Times . . .
Thanks to both who made me laughing . . .
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
The other tutor is in fact right -- ANY next number will make a valid sequence.
So this problem is a puzzle rather than a math problem that can be solved.
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.
One pattern that should be easy to see is that 234 is 6 less than 240 and then 72 is 6 less than 78.
So now look for a relationship between 234 and 78; it turns out that 78 is 234 divided by 3.
So PERHAPS the given numbers follow the pattern "subtract 6; divide by 3; repeat".
So a good guess for the next number is 72/3 = 24.
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....
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".
And the corollary to that is that nobody can tell you that any answer you come up with is wrong....
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For thin-skinned tutor @ikleyn........
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.
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.
Then you laughed at me for "PREDICTING" that the next number was 24.
I did no such thing.
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.
And you laughed at her response, even though it demonstrates a valid mathematical technique.
Neither response was in any way an attempt to "improve" or "disprove" anything you wrote in your post.
Stick to writing good responses to readers' questions and stop trying to make yourself look superior to other tutors.
Answer by MathLover1(20850)  (Show Source):
You can put this solution on YOUR website!
 ,  ,  , 
find differences
........................
......... .......... ...............
............. ..........
................... -> third differences are same, means nth term formula will be
set up the system
 .............eq.1
 .............eq.2
 .............eq.3
 .............eq.4
when you solve the system above, you will get
 ,  ,  , 
and nth term formula is:
the next term is  => 
, , , ,
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