# Iteration

## Find approximate solutions to equations numerically using iteration.

##### FibonacciLevel 1Level 2Level 3Level 4Exam-StyleDescriptionHelpMore Algebra

This is level 2: rearranging equations. You can earn a trophy if you get at least 5 questions correct.

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 1. The equation $$x^2 - 4x + 3 = 0$$ can be arranged to give which of the following iterative formulas?$$x_n = \frac{x_{n-1}^2}{4} + \frac{3}{4}$$$$x_n = \frac{x_{n-1}^2}{4} - \frac{3}{4}$$$$x_n = \frac{x_{n-1}^2}{3} - \frac{4}{3}$$ 2. The equation $$x^2 - 5x + 7 = 0$$ can be arranged to give which of the following iterative formulas?$$x_n = \sqrt{5x_{n-1}+7}$$$$x_n = (5x_{n-1}-7)^2$$$$x_n = \sqrt{5x_{n-1}-7}$$ 3. The equation $$x^2 + 2x - 5 = 0$$ can be arranged to give which of the following iterative formulas?$$x_n = \frac{2}{5} - \frac{x_{n-1}^2}{5}$$$$x_n = \frac{5}{2} - \frac{x_{n-1}^2}{2}$$$$x_n = \frac{5}{2} + \frac{x_{n-1}^2}{2}$$ 4. The equation $$x^3 - x - 9 = 0$$ can be arranged to give which of the following iterative formulas?$$x_n = \sqrt{x_{n-1}-9}$$$$x_n = (x_{n-1}-9)^2$$$$x_n = \sqrt[3]{x_{n-1}+9}$$ 5. The equation $$x^2 + 5x - 2 = 0$$ can be arranged to give which of the following iterative formulas?$$x_n = \frac{2}{5} + \frac{x_{n-1}^2}{5}$$$$x_n = \frac{2}{5} - \frac{x_{n-1}^2}{5}$$$$x_n = \frac{5}{2} + \frac{x_{n-1}^2}{2}$$ 6. The equation $$x^3 - 2x^2 - 3 = 0$$ can be arranged to give which of the following iterative formulas?$$x_n = \sqrt[3]{2x_{n-1}-3}$$$$x_n = (2x_{n-1}^2-3)^2$$$$x_n = \sqrt[3]{2x_{n-1^2}+3}$$
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This is Iteration level 2. You can also try:
Level 1 Level 3 Level 4

## Instructions

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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.

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## Example

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

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