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Iteration

Find approximate solutions to equations numerically using iteration.

Menu Fibonacci Level 1 Level 2 Level 3 Level 4 Exam Help More Algebra

This is level 1: generating sequences using next term rule. You can earn a trophy if you get at least 5 questions correct.

1. A sequence begins with the number 11 and then each of the following terms is 3 more than the previous term. This can be written as \(x_n = x_{n-1} + 3\) where \(x_1 = 11\). What is the second term of this sequence?
2. Find the third term of the sequence given by \(x_n = x_{n-1} + 4\) The first term of the sequence \(x_1 = 14\).
3. Find the fourth term of the sequence given by \(x_n = x_{n-1} - 5\) The first term of the sequence \(x_1 = 13\).
4. Find the fifth term of the sequence given by \(x_n = 2x_{n-1} + 1\) The first term of the sequence \(x_1 = 2\).
5. Find the fifth term of the sequence given by \(x_n = 2x_{n-1}^2 + 2\) The third term of the sequence \(x_3 = 6\).
6. Find the first term of the sequence given by \(x_n = 5x_{n-1} - 7\) The third term of the sequence \(x_3 = 358\).

This is Iteration level 1. You can also try:
Level 2 Level 3 Level 4

Instructions Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help. When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

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Description of Levels

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Fibonacci Probably the first iterative example learners will encounter is the Finonacci sequence. A simple rule exists for finding the next term of the sequence from the previous two.

Level 1 - Generating sequences using next term rule.

Level 2 - Rearranging equations.

Level 3 - Using flowcharts to define iterations.

Level 4 - Solving equations to one decimal place.

Exam Style questions are in the style of GCSE or IB/A-level exam paper questions and worked solutions are available for Transum subscribers.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

Example

The video above is from Steve Blades (https://m4ths.com).

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly.

For an animated demonstration of the calculator button pressing order for iteration see Calculator Workout skill 16.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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