GCSE · Iteration

Using an iterative formulaExam-style questions

How x_{n+1} = g(x_n) feeds each estimate into the next, the full-precision discipline (never round mid-chain), and what the settling sequence tells you about the equation's root.

Start practising Read the lesson

11 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 4 Level 5

1
$x_{n+1} = \sqrt[3]{7x_n + 8}$

Starting with $x_1 = 3$ , the values of $x_n$ get closer and closer to $3.0958\ldots$

(a) Write down a solution, correct to 2 decimal places, of the equation $x^3 - 7x - 8 = 0$

(b) Explain why this value is a solution of the equation $x^3 - 7x - 8 = 0$
Level 5 · 2 marksTry it
2
$x_{n+1} = \sqrt[3]{4x_n + 9}$

(a) Given that $x_3 = 2.68168$ , work out the value of $x_4$ . Give your answer correct to 3 decimal places.

(b) The values of $x_n$ approach a limit. Which equation does that limit satisfy?
Level 5 · 4 marksTry it
3
$x_{n+1} = \sqrt[3]{30 - 2x_n}, \qquad x_1 = 3$

(a) Work out the values of $x_2$ and $x_3$ . Give your answers correct to 4 decimal places.

(b) Explain what the limit of this iteration represents.
Level 5 · 4 marksTry it