1
Start with an initial value x₀
2
Substitute into the iterative formula to find x₁
3
Use x₁ to find x₂, then x₂ to find x₃, etc.
4
Stop when values converge (become very similar)
This deep dive covers How Iteration Works within Iteration for GCSE Mathematics. Revise Iteration in Algebra for GCSE Mathematics with 9 exam-style questions and 3 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 2 of 4 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.
Practice questions for Iteration
What is the purpose of using an iterative formula in mathematics?
A student uses the iterative formula xₙ₊₁ = xₙ² − 2 with x₀ = 0.5 and obtains the sequence 0.5, −1.75, 1.0625, −0.871, −1.241, ... Explain what is happening.
Quick recall flashcards
Iteration Process
Put xₙ into formula to get xₙ₊₁. Repeat until values converge (settle down).
Sum Formula
S_n = a(r^n - 1)/(r - 1) where r is common ratio