An arithmetic (or linear) sequence is a sequence where the difference between successive terms is a constant.

A geometric sequence is a sequence with a constant multiplicative relationship between successive terms.

Checking and securing understanding of non-linear sequences

Maths

Extending thinking about sequences

Exploring the shapes of graphs using technology

Equations and their graphs

Efficiently drawing linear graphs

Reading from graphs

Modelling with graphs

Graphically solving two linear graphs that intersect

Problem solving with graphical representations

In this unit, pupils studied the graphical representation of a geometric sequence and linked features of the graph to its equation. In the future unit, other types of graphs are introduced and their key features identified.

In the prior unit, pupils considered geometric sequences and how they might be represented graphically. In this unit, pupils study the graphical representation to link features of the graph to its equation.

In this unit pupils draw, interpret and utilise linear graphs to solve problems. This knowledge is further extended to look at intersecting graphs.

Graphical representations

A sequence with a multiplicative, term-to-term relationship is called __________ sequence.

Find the common ratio of the geometric sequence 192, 48, 12, ...

What is the common second difference of the sequence 3, 12, 27, 48, ... ?

It is arithmetic. It has a common first difference between terms.

Select the statements that are true of the sequence 2, 16, 54, 128, 250, ...

Which of these sequences will not always decrease?

The sequence -7, -3, 1, 5, 9, ... has a common difference of +4 therefore it is called  __________ sequence.

The sequence 4, 12, 36, 108, ...has a common ratio of ×4 therefore it is called __________ sequence.

Match each arithmetic sequence to its next term.

The next term of this geometric sequence 5, 15, 45, 135, ... is  {{}}.

It is an arithmetic sequence. The differences go -5, -6, -7, -8, ...

It does not have a common difference between terms.

Why is 50, 45, 39, 32, 44, ... not an arithmetic sequence?

Which of these words describes the sequence -86, -74, -62, -50, ... ?

Checking and securing understanding of non-linear sequences

Lesson outcome