All 303 families

GB-41-04-001 · Iteration

Use the iteration xn+1=62−xn3x_{n+1}=\sqrt[3]{62-x_n} with x₀ = 4. Find x₁, x₂ and x₃, each to 4 decimal places. Keep full precision between steps.

Iteration Booklet p. 32
Method
1) Substitute x₀
2) Reuse ANS at full precision
3) Round only the displayed answers to 4 decimal places
Worked Example (GB-41-04-001)
1)
Start with x0=4x_0=4. Enter the cube-root recurrence and use ANS for each subsequent input; retain full calculator precision.
2)
x1=62−43≈3.8709x_1=\sqrt[3]{62-4}\approx3.8709
3)
x2=62−x13≈3.8737x_2=\sqrt[3]{62-x_1}\approx3.8737
4)
x3=62−x23≈3.8737x_3=\sqrt[3]{62-x_2}\approx3.8737
5)
The displayed values are rounded to 4 decimal places; the calculation uses the unrounded previous value.
Ans = x₁ = 3.8709, x₂ = 3.8737, x₃ = 3.8737