UNIT OVERVIEW

Number patterns are everywhere. The rows of seats in a stadium, the pages in your notebook, or the money you save each week—all follow patterns. In this unit, you will learn to find the hidden rules that control sequences of numbers. Once you know the rule, you can predict any term—the 10th, the 100th, or even the 1000th.

By the end of this unit, you will be able to:

• Identify number patterns with a constant difference between consecutive terms
• Calculate the common difference in a linear sequence
• Determine the general term ($T_n$) of any linear sequence
• Use the general term to find any specific term in a sequence
• Determine the position of a term within a sequence
• Apply number patterns to solve real-world problems
• Work backwards from given information to find unknown values

Where you will use number patterns:

• Savings plans: If you save R50 in month 1, R100 in month 2, R150 in month 3, patterns help you calculate your total after any number of months.
• Transport costs: Taxi fares often have a starting fee plus a fixed amount per kilometre—a linear pattern.
• Construction: Builders laying bricks need to calculate how many bricks are needed for walls of different lengths.

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