Chapter 10: Sequences

A sequence is a list of numbers in a pattern. In this chapter, you will describe patterns and find rules for later terms.

The chapter problem: two tile patterns

Two displays use square tiles. Pattern A has $5$ tiles in its first design and adds $3$ tiles each time. Pattern B has $2$ tiles in its first design and doubles each time.

First contact. Without finding exact later totals, predict which pattern will have more tiles in design $5$. You can change your prediction later.

By the end, you will use rules to calculate both totals and decide when Pattern B first has more tiles.

By the end of this chapter you will be able to

• describe how a sequence changes from one term to the next;
• use a position number to calculate a term directly;
• recognise square, cube, triangular and Fibonacci sequences;
• find and use rules for linear, quadratic and geometric sequences.

Your route through the chapter

1. 10.1 Term-to-term and position-to-term rules
2. 10.2 Special sequences
3. 10.3 The nth term of a linear sequence
4. 10.4 The nth term of a quadratic sequence
5. 10.5 Geometric sequences
6. Review

Make a connection

Where have you seen a pattern that grows in steps, such as tile designs, savings, or points in a game? Describe one pattern and say how a rule could help.