**"Geometric series"**

## Years 6 – 12 Sierpinski Number and Shape Patterns

*By toni On 11 September, 2019 · 2 Comments*

In March 2014 and February 2015 Bubblz the Mathematical Clown and the Pyraloons built Guinness World Record breaking Balloon Model Sierpinski Pyramids to raise funds for AIMSSEC. The photo shows the triumphant team in a shopping mall in Cambridge, UK and their 6.5 metre high pyramid.

The smallest pyramid is made from […]

## Years 10 to 12 The von Koch Curve

*By toni On 10 September, 2019 · Leave a Comment*

Image starting with an equilateral triangle and replacing each edge by a zig-zag curve made up of 4 pieces. Each of the 4 pieces is one third of the length of the line segment it replaces so it looks as if equilateral triangles have been attached to the shape. Now imagine repeating […]

## NA5 GROWTH AND DECAY – FINANCIAL MATHEMATICS

*By toni On 28 August, 2018 · Leave a Comment*

This workshop guide provides learning activities that explore the ways in which arithmetic and geometric series are used in simple and compound interest calculations related to loans (including pay-day loans) , investments, annuities, hire-purchase, inflation etc. and there is an explanation of how APR is calculated. Ideas are given for practical ways […]

## Year 12 GP Algebraically

*By toni On 26 May, 2017 · Leave a Comment*

Multiply out these expressions:

What do you notice?

Does this pattern continue?

Can you prove it?

What does this tell you about the sum to n terms of the geometric series with first term 1 and common ratio r?

Why do we get a formula for all values of r except r = 1?

Explain […]

## Grade 12 GP Geometrically

*By toni On 12 January, 2017 · Leave a Comment*

The squares in the diagram are to help us visualise an infinite geometric sum and we are not summing the areas of the squares, simply the lengths along the x-axis. The squares have side lengths given by powers of r: where 0 < r < 1 .

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