Math lesson plan · 11th grade (Year 12 in England) · 30 minutes
Sum a finite geometric series
Algebra
CCSS HSA.SSE.B.4England: A-level Pure Mathematics
Objective and success criteria
Students will: Sum a finite geometric series.
- I can answer questions on today's skill on my own, without help.
- I can explain each step and say why it works.
- I can check my answer and spot a mistake.
Before and after
Needs first: Find the ratio and terms of a geometric sequence
Leads to: Evaluate sums written in sigma notation; Find the sum to infinity of a geometric series
Materials: Balance scales or a balance drawing, Algebra tiles, Function machine cards, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 4 min
- Quick retrieval from earlier learning (Find the ratio and terms of a geometric sequence). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- What is the common ratio of the geometric sequence 5, 15, 45, 135, …? → 3Prompt: Divide a term by the term before it.
- Find the 7th term of the geometric sequence 5, −10, 20, … → 320Prompt: aₙ = a₁ × rⁿ⁻¹.
- Daniel invests $4000. The value is multiplied by 1.1 every year, giving a geometric sequence. What is the value at the start of year 6 (after 5 years)? Round to the nearest whole number. → 6442Prompt: Each year multiplies the value by the same ratio.
Hook · 3 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Sum a finite geometric series. Read the success criteria together.
I do: model it · 7 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: Find the sum of the first 6 terms of 1 + 3 + 9 + …
- Step 1: 1(3^6 − 1)/(3 − 1)
- Step 2: = 364
- Answer: 364
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 6 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- Find the sum of the first 5 terms of 5 − 10 + 20 + … → 55Prompt: Sₙ = a(rⁿ − 1)/(r − 1).
- Arjun saves $5 in week 1 and doubles the amount saved each week. How much has Arjun saved in total after 6 weeks? Give the amount as a number. → 315Prompt: The weekly amounts form a geometric sequence with r = 2.
You do: independent practice · 7 min
- Students work on the student sheet. Circulate and check the first two answers of every student early.
- Students who finish: write a question of their own for a partner, with the answer.
The 6 questions are on the student sheet below, with answers in the key.
Exit ticket · 3 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Find the sum of the first 5 terms of 2 + 4 + 8 + … → 62Prompt: Sₙ = a(rⁿ − 1)/(r − 1).
- Find the sum of the first 7 terms of 128 + 64 + 32 + … → 254Prompt: Here r = 1/2. Use Sₙ = a(1 − rⁿ)/(1 − r).
Watch out for
- Doing an operation to one side of an equation but not the other.
- Reading 3x as 3 + x, or thinking x always stands for one particular number.
Support and stretch
Support
- Review first: Find the ratio and terms of a geometric sequence.
- Use concrete materials: balance scales or a balance drawing.
- Give the first step of each question, or a partly worked example to finish.
- Pair with a confident partner for the guided practice.
Stretch
- Move on to: Evaluate sums written in sigma notation; Find the sum to infinity of a geometric series.
- Explain a common mistake in writing and how to fix it.
- Write a word problem that uses today's skill, then solve a partner's.
Homework and more practice
Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-11.
Free lesson plan from eurekami.com/lesson-plan-builder