Number Patterns
This module covers arithmetic and geometric sequences, first order linear difference equations, Fibonacci and related sequences and the solution of related equations numerically or graphically (algebraic approaches may be used where applicable but are not required).
Arithmetic and geometric sequences:
- Arithmetic sequences and finding terms and the sum of a finite number of terms and applications.
- Geometric sequences and finding terms and the sum of a finite number of terms. Also, applications of geometric sequences including growth models.
- Infinite geometric sequences and the sum of an infinite geometric sequence;
- Comparing arithmetic and geometric sequences through the use of visual aids such as graphs.
Difference equations, including:
- Generation of the terms of a sequence from a difference equation, graphical representation of such a sequence and interpretation of the graph of the sequence;
- Arithmetic and geometric sequences as specific cases of first-order linear difference equations;
- Other first-order linear difference equations used to model change;
- Setting up and using difference equations to represent practical situations such as growth models in various contexts (numerical and graphical solution of related equations);
- Fibonacci and related sequences and applications (numerical and graphical solution of related equations).
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