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.

Extrapolating a sequence

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

Recognising special number sequences

Graphing special number sequences using technology

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

Multiply the previous term by 2 to get the next term.

Add 8 to the previous term to get the next term. 

Add 8, then add 16 then add 24; common second difference of 8.

Add the two prevous terms to get the next term.

Which of these could be a rule for generating the sequence 8, 16, 32, ...?

These are a triangular numbers, they are not a sequence.

There is not a common difference of 5 between successive terms. 

The pattern may change after the fourth term.

Sequences must have a constant additive or multiplicative rule.

Izzy says the next term in the sequence 1, 3, 6, 10, ... must be 15. Why is she incorrect?

Prime numbers over 30 written in ascending order

A sequence which alternates between adding 4 and adding 2

A linear sequence with common difference +4

Sequence of numbers one more than the square numbers

Integers where the digits sum to multiples of 5

Which of these could be a rule for the sequence:  37, 41, 43, 47, 53, ...?

Add 2, add 1, add 0, add -1; common second difference of -1.

Integers greater than 16 where the digits sum to even numbers.

Numbers with nine letters when written in English.

Add the two previous numbers and subtract 10 to get the next number.

Which of these could be the rule for the sequence starting 17, 19, 20, ...?

Linear sequence with a common difference of +2

Sequence which adds 1, then 2, then 3; common second difference of 1

Double the previous term then subtract 5 to get the next term

Number of letters in the English words for days of the week, starting on Monday

Number of letters in the English words for the months starting on August

Which of these could be the rule for the sequence starting 6, 7,  9, ...?

add 3 to the previous term to get the next term.

multiply the previous term by 2 to get the next term.

add 3, add 6, add 9, common second difference of 3.

triple the previous term and subtract 3 to get the next term.

Match each sequence which start with the terms 3, 6, ... to the correct rule.

Add 1, add 3, add 5 and so on, differences increasing by 2 each time.

Add 1, add 7, add 13 and so on, differences increasing by 6 each time.

Add the two previous terms to get the next term.

Multiply the two previous terms to get the next term.

Multiply the previous term by 2 and subtract 1 to get the next term.

 7, 8, 15, 23, 38 ... are the first five terms of a sequence. Which of these could be a rule for the sequence?

A linear sequence starts -4, 6, ... . The next term is {{ }}.

A geometric sequence starts -4, 6, ... . What is the next term?

Which of these could be the first 5 terms in a sequence with a common second difference?

Extrapolating a sequence

Lesson outcome