Topics · Edexcel GCSE Maths (1MA1)

Iteration

Higher only

Iteration is substitution, repeated. Each answer goes back into the formula, and the values close in on a root.

Exam-style questionCalculator allowed3 marks

Using $x_{n+1} = \sqrt[3]{4 - x_n}$ with $x_0 = 1$ , find the values of $x_1$ , $x_2$ and $x_3$ .

Give each answer to 4 decimal places.

See why

Keep iterating. What value does $x_n$ settle on, to 4 decimal places?

$x_{n+1} = \sqrt[3]{4 - x_n}$

Start, x₀1

n	xₙ
0	1

Each value goes back into the formula. Watch the digits stop changing.

New contextCalculator allowed3 marks

The number of fish in a lake is modelled by $P_{n+1} = 1.05P_n - 40$ , where $P_n$ is the number of fish after $n$ years.

$P_0 = 1000$ .

Work out the number of fish after 3 years.

Give your answer to the nearest whole number.

Iterative formulae, roots and growth models

Short hands-on steps, then exam questions on this topic.

Higher tier only.
Usually on a calculator paper, with values to a stated number of decimal places.
Pearson's examiners report accuracy lost by rounding in the middle of a calculation.