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
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.
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.