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 4 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and 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
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.