# Number Sequences and Patterns

Numbers can have interesting patterns. Some of our problem solving strategies can help us figure out the rule of a number pattern or sequence.

There are many different types of number patterns. Just some of the common ones include:

Eg. 2, 4, 6, 8, 10…

Two is added on to each number.

Subtracting

Eg. 35, 30, 25, 20, 15, 10…

Five is subtracted from each number.

Multiplying

Eg. 2, 6, 18, 54, 162…

Each number is multiplied by three.

Mixed Pattern

Eg. 5, 8, 16, 19, 38, 41

In this pattern, three is added and then the number is multiplied by two. It continues + 3, x 2, + 3, x 2….

### What is the rule for these number patterns? Can you leave a comment with the next three numbers in the sequence?

1.  2, 4, 8, 16, 32 …

2. 98, 90, 82, 74, 66 …

3. 181, 184, 187, 190, 193 …

4. 5, 6, 8, 11, 15, 20 …

5. 10, 12, 24, 26, 52, 54 …

## 9 thoughts on “Number Sequences and Patterns”

1. Hi 4KM and 4KJ,
Great post

1.2,4,8,16,32,64,128,256
2.98,90,82,74,66,58,50,42
3.181,184,187,190,193,196,199,202
4.5,6,8,11,15,20,26,33,41
5.10,12,24,26,52,54,108,110,220

From 😛 Darcy 😎

• Hi 4KM and 4KJ,

Oops, I forgot to explain my patterns. Here they are.
1. Double 2 is 4 and double 4 is 8 etc.
2. -8
3. +3
4. You would add on +1 each time. Eg. 5+1=6 6+2=8 8+3=11
5.+2 then double the number, +2 again then double the number etc.

From 😛 Darcy 😎

• Hi Darcy,

Great comment and answer’s. I am not going to answer any so don’t worry about me copying you.

I thought tat this was a great idea as a post and I can’t wait till I gt time to leave one to the grade and explain my answer’s.

I am afraid that, that is all I have time for but I will be back shortly to have another look.

From Olivia

2. Dear 4KM and 4KJ,

I often found looking for patterns fascinating, whether patterns in nature, patterns we make or patterns in mathematics.

Looking at number patterns above, I was able to see the rules but won’t give them away. If you look at your examples above, you might be able to out whether each is a single or mixed pattern.

I have a favourite more complex number sequence. It’s known as the Fibonacci Sequence. Here are the first few numbers…
0, 1, 1, 2, 3, 5, 8, 13, 21, …
Can you see the pattern?
You add the two numbers before each time starting with 0 and 1…
0+1=1, 1+1=2, 1+2=3, 2+3=5, 3+5=8, 5+8=13, 8+13=21, …

There are also triangular number sequences (the dots to make triangle), square number sequences, cube number sequences and others but looking at them all, there is one we all know, one I call the counting number sequence. Can you tell what comes next?
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, _____

Maths, like many subjects, has always interested me and number sequences can be fascinating as you try to work them out. 🙂

Ross Mannell
Teacher (retired), N.S.W., Australia

• Hi Ross,
Is the next number of your third question 14?
We talked about one of your questions for us. It was pretty hard. But our teachers say once we get it it’s not that difficult.

Lots of people got it straight away but some people got it straight away. Well I didn’t get that tricky question straight away. Once I kept on thinking I kind of got it.

Great comment,
Princess

• Hello Princess,

The counting number sequence is one we often use without thinking about it. We use it whenever we count things. The Fibonacci sequence is harder so I know this one is more difficult to solve but once you understand, it becomes easier.

It can be fun to make up a sequence and see if friends can solve it. They can be very hard but, with enough clues, we can solve many although I have seen number sequences I don’t know if I could solve without a great deal of effort and then possibly not get the answer.

Here is a hard sequence I found on a website…
15,29,56,108,208,____
The site gave me four choices for the next number in the series…
a) 386 (b) 400 (c) 416 (d) 438

We could guess the next number but I like to know why we have an answer. The answer is (b) 400.

I wouldn’t expect any of your classmates to know how to work this one out and not just guess. I wonder if you know an adult who can work out how to get the answer?

Here is a link to a post showing how I worked out the answer if you know an adult interested…

Numbers can be fun and are great exercise for our minds. 🙂

Ross Mannell

• Hi Ross,

Hi my name is Charlotte and I am in 4KM and 4KJ.

Thanks for replying to Princess,I will have a look at your extended comment!

Charlotte 😆

• Hi Charlotte,

I spend quite a large amount of time on blogging and blog commenting. There are so many students doing interesting topics in school I can always find something to write about.

Keep blogging,
Ross Mannell

• Hi Ross,