# Sequence Problem: Find Next 3 Numbers

• Natasha1
In summary, this conversation is about a past paper exam question at a school, and the people discussing it have eliminated the constant-difference type of sequence. Ray has found the next three terms in the sequence and suggested looking over class exercises or homework.
Natasha1

## 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?

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?

mfb said:
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...

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

Simon Bridge said:
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

Raiyan said:
I think the answer is 5,-6,-24

I get 11, 16, 28.

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.

LCKurtz said:
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.

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.

## What is a sequence problem?

A sequence problem involves finding the pattern or rule in a series of numbers and using that pattern to determine the next numbers in the sequence.

## What are the common types of sequences?

The common types of sequences include arithmetic sequences, geometric sequences, and Fibonacci sequences.

## How do I find the next numbers in a sequence?

To find the next numbers in a sequence, you need to identify the pattern or rule in the sequence and then use it to determine the next numbers. This can involve basic arithmetic operations, such as addition, subtraction, multiplication, or division, or more complex patterns.

## What are some tips for solving sequence problems?

One tip for solving sequence problems is to look for patterns in the given numbers, such as a repeating sequence of digits or a consistent change in the numbers. Another tip is to try to use basic arithmetic operations to find the pattern or rule, and if that doesn't work, try more complex operations or look for other patterns.

## Why are sequence problems important?

Sequence problems are important because they help develop critical thinking and problem-solving skills. They also have applications in various fields, such as mathematics, computer science, and data analysis.

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