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AlgebraStudy Notes

Worked Example

Part of Iteration — GCSE Mathematics

This study notes covers Worked Example 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 3 of 3 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 3 of 3

Practice

9 questions

Recall

3 flashcards

Worked Example

Use the iteration formula xₙ₊₁ = (xₙ² + 3)/4 with x₀ = 2 to find x₃

Calculate

x₁ = (2² + 3)/4 = (4 + 3)/4 = 7/4 = 1.75

x₂ = (1.75² + 3)/4 = (3.0625 + 3)/4 = 6.0625/4 = 1.515625

x₃ = (1.515625² + 3)/4 = (2.297... + 3)/4 ≈ 1.324

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.

How Iteration WorksZeroing In

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

Sum Formula
S_n = a(r^n - 1)/(r - 1) where r is common ratio
Iteration Process
Put xₙ into formula to get xₙ₊₁. Repeat until values converge (settle down).

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