## Exam-Style Questions on Iteration## Problems on Iteration adapted from questions set in previous exams. |

## 1. | GCSE Higher |

Using \(x_{n+1}=-5-\frac{6}{x_n^2} \)

with \(x_0 = -1.5 \)

(a) find the values of \(x_1, x_2 \) and \(x_3\)

(b) Explain the relationship between the values of \(x_1, x_2 \) and \(x_3\) and the equation \(x^3+5x^2+6=0 \)

## 2. | GCSE Higher |

(a) A sequence is defined by the following rule where \(u_n\) is the \(n^{th}\) term of the sequence:

$$u_{n+1}=u_n^2-5u_n+21$$If \(u_1=3\) find \(u_2\) and \(u_3\).

(b) A different sequence is defined by the following rule:

$$u_{n+1}=u_n^2-8u_n+17$$If \(u_1=5\) find \(u_2\) and \(u_3\) and \(u_{50}\).

## 3. | GCSE Higher |

Consider the following cubic equation:

$$x^3-7x-5=0$$

An approximate solution can be found by using the following iterative process.

$$x_{n+1}=\frac{(x_n)^3-5}{7}$$(a) Find \(x_2\) and \(x_3\) if \(x_1=-1\)

Work out the solution to 6 decimal places.

The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.

The solutions to the questions on this website are only available to those who have a Transum Subscription.

Exam-Style Questions Main Page

To search the **entire Transum website** use the search box in the grey area below.

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.

Kausar Begum Khan, Kenya

Friday, January 26, 2018

"This is a fabulous website! I cannot thank you enough."

Aruna Upadhyayula, Bahrain

Tuesday, November 6, 2018

"Transum is so resourceful. The resources are so child-friendly that my students love its usage.It has a wide range of topics and caters to most of my needs. 'Thankyou" will be too small a word to express my gratitude to the content developers of this site."

Ahmed Jaja, Ghana

Thursday, November 22, 2018

"It was very useful for me.I recommend it to every math student.Thank you."

Madiwa Otieno, Kenya

Tuesday, February 5, 2019

"A very great site.Nice questions."