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

Features of 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

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

Starting with the smallest triangular number, order these numbers so they form the sequence of triangular numbers in ascending order.

Which of these arrays correctly represents a triangular number?

The $$n^{\text{th}}$$ term rule for a sequence is $$n^{2}$$. The $$8^{\text{th}}$$ term in the sequence is {{}}.

The $$13^{\text{th}}$$ triangular number is 91. The $$14^{\text{th}}$$ triangular number is {{}}.

$$4^{th}$$ square number + $$2^{nd}$$ cube number 

$$1^{st}$$ triangular number + $$11^{th}$$ square number

$$9^{th}$$ triangular number + $$10^{th}$$ triangular number

$$5^{th}$$ cube number + $$5^{th}$$ triangular number

$$6^{th}$$ square number − $$7^{th}$$ triangular number 

$$8^{th}$$ square number − $$4^{th}$$ cube number 

Match each answer to the correct calculation.

The hexagonal numbers are made by arranging dots on hexagonal shapes. Using the diagram, the $$5^{\text{th}}$$ hexagonal number is {{ }}.

Which of these arrays represent a square number?

multiply previous term by 3 to get the next term

add 8 to the previous term to get the next term

add 8, then add 10, increasing the difference by 2 each time

add 8, then add 9, increasing the difference by 1 each time

multiply the previous term by 2 and add 4 to get the next term

Match each sequence with its term-to-term rule.

Which of these could be a position-to-term rule for the sequence which starts 5, 8, 11, 14, 17, ... ?

Which of these could be the first 4 terms of a geometric sequence?

Features of special number sequences

Lesson outcome