UNIT OVERVIEW

Patterns, sequences, and series appear throughout mathematics and everyday life. They describe how savings accounts grow, how populations change, and how payments add up over time. In this unit, you will build on your Grade 11 knowledge to derive formulas, use sigma notation, and work with infinite series.

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

• Work confidently with arithmetic and geometric sequences
• Use and interpret sigma notation (∑) to express and calculate sums
• Derive the formula for the sum of an arithmetic series from first principles
• Derive the formula for the sum of a geometric series from first principles
• Apply these formulas to solve real-world problems
• Determine when a geometric series converges and calculate its sum to infinity
• Solve problems involving simultaneous equations with sequences

Where you will use this:

• Savings and investments: Monthly deposits form a sequence; the total saved is a series.
• Depreciation: A car loses value by a percentage each year—this follows a geometric sequence.
• Medicine dosage: Drug levels in the body can be modelled using geometric series.
• Seating design: Rows with increasing seats follow arithmetic sequences.

---