Free Maths Calculator

Iteration Calculator

Run a GCSE Higher iteration formula from a starting value and watch it settle. Pick the shape of formula, type its two numbers and x₀, and every iteration is listed in a table until two results in a row round to the same answer. A sign change check then confirms the root is correct.

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Method, Step by Step

    Worked Example

    Use xₙ₊₁ = ∛(2xₙ + 5) with x₀ = 2 to find a solution to 2 decimal places.

    1. x₁ = ∛(2 × 2 + 5) = 2.080084
    2. x₂ = ∛(2 × 2.080084 + 5) = 2.092351
    3. x₃ = ∛(2 × 2.092351 + 5) = 2.094217
    4. x₂ and x₃ both round to 2.09, so stop

    Answer: x = 2.09

    Try These Yourself

    Use xₙ₊₁ = 3 + 1 ÷ xₙ with x₀ = 3. Find x₁ and x₂.Show answerHide answer

    Answer: x₁ = 3.3333, x₂ = 3.3

    3 + 1 ÷ 3 = 3.3333, then 3 + 1 ÷ 3.3333 = 3.3.

    Which equation does xₙ₊₁ = √(xₙ + 6) solve?Show answerHide answer

    Answer: x² − x − 6 = 0

    Square both sides of x = √(x + 6): x² = x + 6.