Patterns

A sequence is a set of numbers that are connected in some way. In this section, we will learn how to recognise different types of sequences, extend a number or diagrammatic pattern and determine its formula.

A sequence is a list of numbers. The numbers are called the terms of the sequence.

There are many well-known sequences of numbers which you should be able to recognise.

Even numbers

\[2,\,4,\,6,\,8,\,10,\,12...\]

Odd numbers

\[1,\,3,\,5,\,7,\,9,\,11...\]

Square numbers

\[1,\,4,\,9,\,16,\,25,\,36,\,49,\,64...\]

(\(1\times 1,\ 2\times2,\ 3\times3\)...)

Cube numbers

\[1,\,8,\,27,\,64,\,125...\]

(\(1 \times 1 \times 1\), \(2 \times 2 \times 2\), \(3 \times 3 \times 3\)...)

Powers of 2

\[2,\,4,\,8,\,16,\,32,\,64...\]

Powers of 10

\[10,\,100,\,1000,\,10000,\,100000,\,1000000...\]

Triangle numbers

\[1,\,3,\,6,\,10,\,15,\,21,\,28...\]

Red dots that are grouped in series of 1, 3, 6, 10, 15, 21