Number Patterns and Recursion

Topic/AOS Overview

This topic includes:

Number patterns and sequences

• the concept of a sequence as a function

• use of a first-order linear recurrence relation to generate the terms of a number sequence

• tabular and graphical display of sequences.

The arithmetic sequence

• generation of an arithmetic sequence using a recurrence relation, tabular and graphical display; and the rule for the nth term of an arithmetic sequence and its evaluation

• use of a recurrence relation to model and analyse practical situations involving discrete linear growth or decay such as a simple interest loan or investment, the depreciating value of an asset using the unit cost method; and the rule for the value of a quantity after n periods of linear growth or decay and its use.

The geometric sequence

• generation of a geometric sequence using a recurrence relation and its tabular or graphical display; and the rule for the nth term and its evaluation

• use of a recurrence relation to model and analyse practical situations involving geometric growth or decay such as the growth of a compound interest loan, the reducing height of a bouncing ball, reducing balance depreciation; and the rule for the value of a quantity after n periods of geometric growth or decay and its use.

Assessment Tasks Overview

• Sequences and Recurrence SAC

Learning Goals/Success Criteria

Chapter 8 Number patterns and Recursion

Other Activities/Excursions