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

A common ratio is a key feature of a geometric sequence. The constant multiplier between successive terms is called the common ratio.

Representing geometric sequences graphically

Maths

Checking understanding of arithmetic sequences

Securing understanding of arithmetic sequences

Features of geometric sequences

Recognising geometric sequences

Features of special number sequences

Recognising special number sequences

Graphing special number sequences using technology

Extrapolating a sequence

Problem solving with non-linear relationships

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

In the sequences unit, pupils learnt how to graphically represent an arithmetic sequence. In this unit, pupils now consider geometric sequences and how these can be represented graphically.

In this unit we explore geometric and special number sequences like the Fibonacci sequence. We develop strategies to recognise types of sequence and continue them.

Non-linear relationships

This graph of $$n$$ (term number) against $$T$$ (term value) could represent which of these types of sequences?

Jacob plots the graph of this geometric sequence. Which coordinates should Jacob plot?

How do you know that this graph might represent a geometric sequence?

What do you know about the common ratio of this geometric sequence?

Which of the below could be the ratio of this geometric sequence?

You can draw a line through the points of this geometric sequence because it is modelling data that is ...

Which type of sequence is represented by this graph?

It has a common additive difference between successive terms.

It has a constant multiplicative relationship between successive terms.

How can you tell that the sequence 17, 24, 31, 38, 45, ... is arithmetic?

How can you tell that the sequence 0.02, 0.2, 2, 20, 200, ... is geometric?

Sofia plots the graph of this arithmetic sequence. Which of these coordinates should Sofia plot?

Which of these will be one of the first five terms in the geometric sequence that has a first term of 1.25 and a common ratio of 2?

The missing $$2^{\text{nd}}$$ term of this geometric sequence is {{}}.

Representing geometric sequences graphically

Lesson outcome