Start with the first two numbers there are: 0, and 1.
Add them together to get the next number in the sequence: 1
You now have the first three terms: 0, 1, 1
Take the last two numbers (1 and 1) and add them together to get the next number in the sequence: 2
You now have the first four terms: 0, 1, 1, 2
Again take the last two numbers (1 and 2) and add them together to get the next number in the sequence: 3
You now have the first five terms: 0, 1, 1, 2, 3
Again take the last two numbers (2 and 3) and add them together to get the next number in the sequence: 5
You now have the first six terms: 0, 1, 1, 2, 3, 5
And so on: 0, 1, 1, 2, 3, 5, 8, 13, 21...

Also look out for sequences which use the same process but add something to each term. For example, this one adds 10 to each term:
(0+10), (1+10), (1+10), (2+10), (3+10), (5+10) and so on, to give...
10, 11, 11, 12, 13, 15, 18, 23, 31...

Other variations are possible.

Triangular sequence
This is the sequence of "triangular numbers" – numbers which can be shown as a set of dots in a triangle.
Start with 1. (That's your first term.)
Add the next number, which is 2: 1+2=3. (3 is your second term)
Add the next number, which is 3: 1+2+3=6. (6 is your third term)
Add the next number, which is 3: 1+2+3+4=10. (10 is your fourth term)
And so on...
1, 3, 6, 10, 15, 21, 28

## Number sequences

Fibonacci sequenceStart with the first two numbers there are: 0, and 1.

Add them together to get the next number in the sequence: 1

You now have the first three terms: 0, 1, 1

Take the last two numbers (1 and 1) and add them together to get the next number in the sequence: 2

You now have the first four terms: 0, 1, 1, 2

Again take the last two numbers (1 and 2) and add them together to get the next number in the sequence: 3

You now have the first five terms: 0, 1, 1, 2, 3

Again take the last two numbers (2 and 3) and add them together to get the next number in the sequence: 5

You now have the first six terms: 0, 1, 1, 2, 3, 5

And so on: 0, 1, 1, 2, 3, 5, 8, 13, 21...

Also look out for sequences which use the same process but add something to each term. For example, this one adds 10 to each term:

(0+10), (1+10), (1+10), (2+10), (3+10), (5+10) and so on, to give...

10, 11, 11, 12, 13, 15, 18, 23, 31...

Other variations are possible.

Triangular sequenceThis is the sequence of "triangular numbers" – numbers which can be shown as a set of dots in a triangle.

Start with 1. (That's your first term.)

Add the next number, which is 2: 1+2=3. (3 is your second term)

Add the next number, which is 3: 1+2+3=6. (6 is your third term)

Add the next number, which is 3: 1+2+3+4=10. (10 is your fourth term)

And so on...

1, 3, 6, 10, 15, 21, 28

See also: