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

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

A triangular number is a number that can be represented by a pattern of dots arranged into an equilateral triangle. The term number is the number of dots in a side of the triangle

Recognising special number sequences

Maths

Checking understanding of arithmetic sequences

Securing understanding of arithmetic sequences

Features of geometric sequences

Recognising geometric sequences

Representing geometric sequences graphically

Features of 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 next term in the sequence 8, 2, 10, 12, ... is found by adding the two previous terms. The next term is {{}}.

$${4\over 3}, {3\over 2}, {5\over 3}, {11\over 6}, ...$$

$${1\over 8}, {1\over 4}, {1\over 2}, {3\over 4}, ...$$ 

Which of these could be an arithmetic sequence?

Which of these could be a geometric sequence?

sequence which starts by adding $$a$$ with second difference $$+a$$

linear sequence with common difference $$2a$$

geometric sequence with common ratio $$a$$

linear sequence with common difference $$a + 1$$

Match the first four terms of each sequence with the rule which could describe it. 

This sequence starts by adding 5 and has a common second difference of 3. The next term in the sequence is {{ }}.

Which of these could be the first four terms of a sequence with a common second difference? (They are called quadratic sequences).

Which of these could be the first four terms in an arithmetic sequence?

 6, 30, 150, 750, ... are the first four terms in a geometric sequence with common ratio {{}}.

36, 49, 64, 81, ... are the first four terms in a sequence of square numbers. The next term is {{ }}.

Select the expression that represents 4 more than $$a + 4$$.

Which of these could be the first four terms in a geometric sequence?

Recognising special number sequences

Lesson outcome