Lesson Plan

• Identify whether a given sequence is an arithmetic progression (AP) or a geometric progression (GP).
• State and apply the nth‑term formulas for AP and GP.
• Calculate the sum of the first n terms for AP and GP and recognise the condition for an infinite GP sum.
• Explain the key differences between APs (additive) and GPs (multiplicative).

• Whiteboard and markers
• Projector or interactive display
• Printed worksheet with progression examples
• Calculators (or classroom calculators)
• Index cards containing number sequences
• Teacher’s note cards with AP and GP formulas

Show a quick visual of equally spaced points versus exponentially spaced points on a number line to spark curiosity. Review the concept of a sequence and recall earlier work on linear patterns. Explain that today’s success criteria are to correctly classify a sequence, write the appropriate nth‑term formula, and compute sums.

1. Do‑now (5'): Students complete a short task identifying patterns in three displayed sequences.
2. Mini‑lecture (10'): Define AP and GP, introduce common difference d and common ratio r, and present the nth‑term formulas.
3. Guided practice (12'): Work through Example 1 (AP) and Example 2 (GP) together, highlighting identification steps and formula use.
4. Collaborative activity (10'): In pairs, students use index cards to determine the type of progression for new sequences and calculate the 10th term or sum as required.
5. Whole‑class discussion (8'): Groups share answers; teacher clarifies common mistakes (confusing d and r, misapplying formulas).
6. Exit ticket (5'): Each student writes the progression type for a given sequence, the correct formula, and one key difference between AP and GP.

Recap that APs involve constant addition while GPs involve constant multiplication, and that the appropriate formulas depend on the identified type. Highlight the condition |r| < 1 for an infinite GP sum. Collect exit tickets and assign homework to complete additional practice questions from the worksheet.