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.

Features of geometric sequences

Maths

Checking understanding of arithmetic sequences

Securing understanding of arithmetic sequences

Recognising geometric sequences

Representing geometric sequences graphically

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

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

The next term in this geometric sequence 7, 14, 28, ... is {{}}.

Which of these numbers will be a term in the geometric sequence: "Start on 2 and use a common multiplier of 5"?

Which of these numbers will be terms of the geometric sequence: "Start on $$432$$ and use a common multiplier of $$1\over2$$"?

The terms will oscillate between positive and negative.

The $$1^{\text{st}}$$ term of a geometric sequence is not zero and the common ratio is negative. Which of these statements is true about this sequence?

If a numerical sequence does not have a common additive difference then you can say it is ...

Which of these sequences are not arithmetic sequences?

What is the result when you multiply $$3$$ by $$5$$ four times? You can use a calculator.

Use your calculator to halve $$80$$ then find half of your result and then halve it again. The result is {{}}.

What number should be written in the box in these equivalent ratios? {{}}.

Features of geometric sequences

Lesson outcome