A triangular number (or triangle number) is a number that can be represented by a pattern of dots arranged into a triangle.

Graphing special number sequences using technology

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

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 sequence with $$n^{th}$$ term $$5.6n + 12$$ is graphed in the diagram. Is 40 a term in the sequence?

The 4th term in the sequence $$3\times 5^{n-1}$$ is {{ }}. Use Desmos or the diagram to help you.

Yes, because $$\sqrt[3]654$$ is an integer.

No, because the graphs do not intersect at an integer $$x$$ value.

No, because 654 is not on the curve with equation $$y = n^3$$.

Is the number 654 in the sequence with $$n^{\text{th}}$$ term rule $$n^3$$? Use Desmos or the diagram to help you.

The sequence has integer term numbers so the curve should not be drawn.

This should be a linear graph not a curve.

The $$y$$ axis scale is double the scale on the $$x$$ axis.

Sequences start when $$n$$ is 1 so there should not be coordinates when $$x<1$$.

Why does this diagram not represent the sequence of all square numbers in ascending order?

The 6th term in both sequences is the same.

The 8th term in both sequences are the same.

This graph shows the sequence of triangular numbers and the sequence $$4n +4$$ (the line and curve are drawn to help you). Which of these statements are true?

Which is the correct $$n^{\text{th}}$$ term rule for the geometric sequence which starts 1, 2, 4, 8, 16, ...?

Which of these is the $$n^{\text{th}}$$ term rule for the linear sequence 6, 10, 14, 18, ...?

Sam draws a graph of this geometric sequence. Which of these coordinates should Sam plot?

Andeep plots the graph of the equation $$y=3.4x-10$$. When the $$y$$ coordinate is $$75$$, the $$x$$ coordinate is {{ }}.

Starter Quiz

Which of these are square numbers?