AlgebraDeep Dive

How Iteration Works

Part of Iteration · GCSE GCSE Mathematics revision

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.

Topic position

Section 2 of 4

Practice

9 questions

Recall

3 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)

Keep building this topic

Read this section alongside the surrounding pages in Iteration. That gives you the full topic sequence instead of a single isolated revision point.

Zeroing In Worked Example Knowledge Organiser: Iteration

Practice Questions for Iteration

What is the purpose of using an iterative formula in mathematics?

A. To find exact algebraic solutions to equations
B. To get increasingly accurate numerical approximations to solutions
C. To factorise quadratic expressions
D. To draw graphs of functions

1 markfoundation

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.

2 marksstandard

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

9 questions on Iteration — practise free

Instant marking, adaptive difficulty, and 3 spaced repetition flashcards. Free until your GCSEs.

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Zeroing In

Worked Example