Iteration
- Start with the given value.
- Substitute into the iteration formula.
- Repeat to improve the estimate.
Answer: If x₁=1 and xₙ₊₁=xₙ+2, then x₂=3
𝑥 Algebra
Iteration
Learn iteration with a GCSE-style explanation, help guide, worked example, practice question and flashcards.
Global XP
Level 10 / 100 XP
1. Explanation
Key idea
- Iteration is part of advanced topics and appears often in KS3–GCSE maths.
- Iteration repeatedly uses a formula to get closer to a solution.
- Use the worked model, help guide, interactive question and flashcards to practise iteration until the steps feel automatic.
Real-life examples
- Shopping, sport, travel, science, design and everyday decisions all use this skill.
2. Visual
Iteration learning map
Understand the key idea → follow the help guide → practise a question → check your method → build speed with flashcards.
3. Help guide
How to tackle Iteration
- Learn the rule: Iteration repeatedly uses a formula to get closer to a solution.
- Worked model: Start with the given value. Substitute into the iteration formula. Repeat to improve the estimate.
- Try the interactive question without looking at the answer first.
- Use the flashcards to test the rule, the method and a common check.
4. Worked examples
Step-by-step working
5. Interactive questions
Try it yourself
Use x₁ = 2 in xₙ₊₁ = (xₙ + 6)/2. Find x₂.
6. Flashcards
Master quick recall
Flip each card, then choose whether you know it or need more practice.
0 mastered
FrontRule for Iteration
BackIteration repeatedly uses a formula to get closer to a solution.
FrontExample answer: Use x₁ = 2 in xₙ₊₁ = (xₙ + 6)/2. Find x₂.
Backx₂ = (2 + 6)/2 = 8/2 = 4.
FrontCommon check for Iteration
BackCheck units/notation, compare with an estimate, and make sure the answer matches the question.
7. Finish
Complete this topic
When you have read the examples, tried the question and reviewed flashcards, claim your topic completion XP.