# Sequence problem

1. Nov 7, 2014

### Natasha1

1. The problem statement, all variables and given/known data
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?

2. Nov 7, 2014

### Staff: 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?

3. Nov 7, 2014

### Natasha1

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.

4. Nov 7, 2014

### Natasha1

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

It is unusable for me...

5. Nov 7, 2014

### Simon Bridge

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

6. Nov 7, 2014

### Natasha1

It is a past paper exam question at my school...

7. Nov 7, 2014

### Raiyan

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

8. Nov 7, 2014

### Ray Vickson

I get 11, 16, 28.

9. Nov 7, 2014

### LCKurtz

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

Last edited: Nov 7, 2014
10. Nov 7, 2014

### Raiyan

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.

11. Nov 7, 2014

### Staff: Mentor

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.

12. Nov 7, 2014

### Simon Bridge

... 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.