Sequences
We see sequences and patterns in many parts of our daily lives. A periodic sequence is a type of pattern that repeats again and again in the same order. Think of the four seasons, the days of the week, or a pattern on wallpaper. When we notice these sequences, it helps us see regularity and guess what will come next.
Sometimes a sequence is made with shapes or colours. In mathematics, many important sequences are made with numbers. These number sequences follow a rule that tells us how to get from one number to the next.
Sometimes a sequence is made with shapes or colours. In mathematics, many important sequences are made with numbers. These number sequences follow a rule that tells us how to get from one number to the next.
Periodic Sequence
Definition Periodic Sequence
A periodic sequence is a sequence in which the elements repeat in a regular, predictable cycle. This cycle can be made of shapes, colours, sounds, numbers, or any other type of element.
Example
Based on the repeating pattern, what is the colour of the next balloon in the sequence?
The color of the next balloon is red. The sequence follows a simple repeating pattern: red colour, blue colour, red colour, blue colour, and so on.
Numerical Sequence
Definition Numerical Sequence
A numerical sequence is a list of numbers in a special order. Each number in the sequence is called a term, and the terms follow a rule that tells us how to find the next number.
Example
What is the next number in the sequence?$$0, 1, 2, 3, 4, ?$$
The next number in the sequence is \(5\). In this sequence, we start at \(0\) and each time we add \(1\) to get the next number.