- Understand the limiting behaviour as n approaches infinity in a geometric sequence and its dependence on the value of the common ratio (ACMMM074)
- Use geometric sequences in contexts involving geometric growth or decay, such as compound interest. (ACMMM076)
About the Lesson
Students begin by exploring the Pebbling the Chessboard problem. It is not long before students challenge whether or not the problem has a solution. Rather than continuing with trial and error attempts, numbers are used to record the moves, leading to the discovery that a geometric sequence is produced. The sum of the terms in the sequence holds the answer to the problem.
A PowerPoint file is also included so that teachers can demonstrate the problem (and solution) to students.