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

Recognising geometric sequences

Maths

Checking understanding of arithmetic sequences

Securing understanding of arithmetic sequences

Features of 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

The constant multiplier between successive terms in a geometric sequence is called the common {{}}.

The common ratio of the geometric sequence 7, 28, 112, 448, 1792, ... is {{ }}.

312, 2184, 15 288, 107 016, 749 112, ... is a geometric sequence. Which of these divisions will give you the common ratio?

Match each geometric sequence to its common ratio.

The first term of this geometric sequence is {{}}.

What could the third term of this geometric sequence be?

__________ sequence is a sequence with a constant multiplicative relationship between successive terms.

In the geometric sequence 1.2, 4.8, 19.2, 76.8, ..., the common __________ between the terms is 4.

Find the next two terms in this geometric sequence: 3, 30, 300, ...

Which of these are terms in the geometric sequence generated by the rule: "Start on $$224$$ and use a common ratio of $$1\over4$$"?

Some of these sequences are geometric, some are arithmetic. Select all the geometric sequences.

It is geometric because the multipliers are: ×2, ×3, ×4, ×5

It has no common ratio therefore it is not geometric.

Which statement is true of the sequence 1, 2, 6, 24, 120, ... ?

Recognising geometric sequences

Lesson outcome