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

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

Extending thinking about sequences

Maths

Checking and securing understanding of non-linear 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

In mathematics, sequences can be described as concrete or __________.

In 1980, the world marathon record was 2 hrs 10 mins. In the year 2000, it was 2 hrs 5 mins. In the year 2020, it was 2 hrs 0 mins. This is an example of  __________ sequence.

It is not limited. The pattern will continue at -5 minutes per decade.

Records are decreasing now but can never reach zero. There are physical limits.

The record of 2hrs 0 mins cannot be broken.

In 1980, the world marathon record was 2 hrs 10 mins. In the year 2000, it was 2 hrs 5 mins. In the year 2020, it was 2 hrs 0 mins. Why is this concrete sequence limited?

What value would come before this geometric sequence? 196, 1372, 9604, 67 228, ...

Scientists begin to study the population of a particular fish in the North Sea and find it forms a geometric sequence. Using the sequence to predict the population for year 5.

Scientists begin to study the population of a particular fish in the North Sea and find it forms a geometric sequence. Estimate the population of the fish the year before the study began.

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

Find the next term in the arithmetic sequence -25, -18, -11, -4,{{}}.

Find the missing term in the arithmetic sequence 27, {{}}, 55, 69, 83, ... 

Find the common ratio of the geometric sequence 0.4, 1.6, 6.4, 25.6, ...

Find the next term in the geometric sequence 0.4, 1.6, 6.4, 25.6, {{ }}, ... Give your answer as a decimal.

It is a decreasing sequence therefore will contain negative values in the future

It is a geometric sequence with a common ratio greater than 1

It is a geometric sequence with a common ratio less than 1

It will eventually start to increase again.

Which statements are true of the sequence 1920, 960, 480, 240, 120, ... ?

Extending thinking about sequences

Lesson outcome