Lesson Plan

• Describe the general term and common difference/ratio of arithmetic and geometric progressions.
• Calculate the sum of a finite arithmetic or geometric series and determine convergence of an infinite geometric series.
• Apply the binomial theorem to expand a binomial and identify specific coefficients using Pascal’s triangle.
• Solve applied problems that require selecting and using the appropriate series formula.

• Projector and screen
• Whiteboard and markers
• Worksheet with AP, GP and binomial practice questions
• Calculator for each student
• Printed handout of key formulae and Pascal’s triangle
• Sticky notes for exit tickets

Start with a quick “what comes next?” puzzle to spark curiosity about patterns. Review students’ prior knowledge of linear sequences and exponentials. Explain that by the end of the lesson they will be able to write formulas, compute series sums, and expand binomials confidently.

1. Do‑now (5') – Pattern identification worksheet on arithmetic vs. geometric sequences.
2. Direct instruction on AP (10') – Definition, nth‑term formula, sum formula, worked example.
3. Guided practice AP (8') – Students calculate a sum using the formula; teacher checks understanding.
4. Direct instruction on GP (10') – Definition, nth‑term, finite‑sum formula, infinite‑sum condition, example.
5. Guided practice GP (8') – Small‑group work on a finite and an infinite GP problem.
6. Mini‑lecture on Binomial Theorem (10') – Statement, Pascal’s triangle, general term, example expansion.
7. Collaborative practice (10') – Students solve selected practice questions from the source notes.
8. Check for understanding (5') – Quick quiz on key formulas; discuss common errors.

Summarise the three core formula families and highlight how they connect to real‑world problems. Ask students to write one formula and a brief example on a sticky note as an exit ticket. Assign the remaining practice worksheet for homework, encouraging students to attempt all five challenge questions.