Iterative methods
Use iteration and the Newton-Raphson method to find approximate roots; cobweb and staircase diagrams
What you'll learn
- 1
Imagine trying to find where a rollercoaster track crosses a fence. You guess a point, then use the slope to get closer and closer — that's iteration! 🎢
- 2
What do we call each repeated step in an iterative method?
- 3
Let's solve x² = 5 using iteration. We'll use the formula xₙ₊₁ = (xₙ + 5/xₙ)/2, starting with x₀ = 2.
- 4
Use the iteration formula xₙ₊₁ = (xₙ + 7/xₙ)/2, starting with x₀ = 2, to find x₁. Type your answer.
- 5
If x₀ = 3 and the formula is xₙ₊₁ = (xₙ + 10/xₙ)/2, what is x₁?
- 6
Now try a harder one: solve x³ = 20 using xₙ₊₁ = (2xₙ + 20/xₙ²)/3, starting with x₀ = 2.5.
- 7
After many iterations, xₙ gets closer and closer to the real answer. What do we call that value?
Practise Iterative methods with Whizlo
Free AI-tutored lessons, unlimited practice questions, and progress tracking for ages 16–18. Aligned to the UK National Curriculum.