For example, 12, -73, 179.347, -84, , or , or any other number.
The posed question is mathematically nonsensical.
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It is also nonsensical from the COMMON SENSE point of view.
Only those who read tooooooo many puzzle books, to the detriment to their mind health,
may believe that "some number should go next in an arbitrary sequence".
No ONE NUMBER has obligation to be next : the sequences has a FREE WILL to carry any number as the next number
until a pattern is defined.
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....
