# Sequence problem

## Homework Statement

Find the next three numbers in this sequence... 4, 16, 21, 21, 18, 14, 11, ...

2. The attempt at a solution
The difference between each term is 12, 5, 6, 0, -3, -4, -3 but I can't see a pattern and I am completely stuck... Any help pls?

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mfb
Mentor
It follows a third-order polynomial, but that would be a weird solution.
Those questions are always problematic, because you can find rules for arbitrary sequences. Even for a sequence that starts like yours and then goes to 1000 for the next three numbers.

Could there be a typo somewhere?

It follows a third-order polynomial, but that would be a weird solution.
Those questions are always problematic, because you can find rules for arbitrary sequences. Even for a sequence that starts like yours and then goes to 1000 for the next three numbers.

Could there be a typo somewhere?
I have doubled and tripled checked... it is indeed , 16, 21, 21, 18, 14, 11, ... and the question is find the next three terms in the given sequence.

sorry 4, 16, 21, 21, 18, 14, 11, ...

It is unusable for me...

Simon Bridge
Homework Helper
What is the context?
i.e. is it a homework assignment or something as part of some coursework?

What is the context?
i.e. is it a homework assignment or something as part of some coursework?
It is a past paper exam question at my school...

I think the answer is 5,-6,-24

Ray Vickson
Homework Helper
Dearly Missed
I think the answer is 5,-6,-24
I get 11, 16, 28.

LCKurtz
Homework Helper
Gold Member
I agree with Ray. And for good measure the next term after his is 59.
[Edit:] Arithmetic mistake: 49. Thanks mfb.

Last edited:
Ray is correct I revised the way I did the math and I see where I went sour. The following 3 numbers are: 11, 16, 28. I apologize for misleading people and posting the wrong answer. I did it by first finding the differences of the original numbers in the sequence. (12,5,0,-3,-4,-3.) Next you find the difference of the numbers that are the difference of the sequence. Finally you find the pattern in -7,-5,-3,-1,1,3,5 (the difference of the numbers that are the difference of the numbers in the sequence.) It sounds more complicated than it is.

mfb
Mentor
I agree with Ray. And for good measure the next term after his is 59.
I think you mean 49.
Well, the number of parameters is lower than the number of sequence elements we have, but still... that rule is quite complicated. And there is always a rule like that, if you calculate the differences long enough.

Simon Bridge
Homework Helper
It is a past paper exam question at my school...
... OK, the trick is to relate the question to the kids of problems you've done in school.
If the past exam paper is more than a couple of years past, though, it may be that the type of sequence they want you to think up has changed since then.

You have already eliminated the constant-difference type... any others you've seen examples of?
Look over class exercises or homework.

To a certain extent, this sort of problem is like "guess the number I just thought of"... so you need a way to narrow down what is possible.
Note: when you plot $x_n$ vs $n$ it does kinda look like it's trying to be a cubic or some fancy exponential. If you have seen sequences like $x_n=P_m(n)$ (Where $P_n(x)$ is a polynomial in x of order n) then that is one way to go.

You could also attempt to decipher the clues in Ray and LC's posts.