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.
How Iteration Works
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)
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