Patterns are all around us!
Finding and understanding patterns gives us great power. With patterns we can learn to predict the future, discover new things and better understand the world around us.
And playing with patterns is fun.
Arithmetic Sequences
An Arithmetic Sequence is made by adding the same value each time.
Example
| 1, 4, 7, 10, 13, 16, 19, 22, 25, … |
This sequence has a difference of 3 between each number.
The pattern is continued by adding 3 to the last number each time, like this:
Geometric Sequences
A Geometric Sequence is made by multiplying by the same value each time.
| 1, 3, 9, 27, 81, 243, … |
This sequence has a factor of 3 between each number.
The pattern is continued by multiplying by 3 each time, like this:
Square Numbers
| 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, … |
They are the squares of whole numbers:
0 (=0×0)
1 (=1×1)
4 (=2×2)
9 (=3×3)
16 (=4×4)
etc…
Cube Numbers
| 1, 8, 27, 64, 125, 216, 343, 512, 729, … |
They are the cubes of the counting numbers (they start at 1):
1 (=1×1×1)
8 (=2×2×2)
27 (=3×3×3)
64 (=4×4×4)
etc…
Fibonacci Numbers
| 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, … |
The Fibonacci Sequence is found by adding the two numbers before it together.
The 2 is found by adding the two numbers before it (1+1)
The 21 is found by adding the two numbers before it (8+13)
The next number in the sequence above would be 55 (21+34)
Can you figure out the next few numbers?
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