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Use the formula $x_{n+1} = \frac{(x_n)^3}{30} + 2$ with $x_1 = 2$ to calculate $x_2$ and $x_3$ - OCR - GCSE Maths - Question 15 - 2018 - Paper 6

Question 15

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Use the formula $x_{n+1} = \frac{(x_n)^3}{30} + 2$ with $x_1 = 2$ to calculate $x_2$ and $x_3$. Round your answers correct to 4 decimal places.

Worked Solution & Example Answer:Use the formula $x_{n+1} = \frac{(x_n)^3}{30} + 2$ with $x_1 = 2$ to calculate $x_2$ and $x_3$ - OCR - GCSE Maths - Question 15 - 2018 - Paper 6

Step 1

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Answer

To find $x_2$ , we use the formula:

$x_2 = \frac{(x_1)^3}{30} + 2$

Substituting $x_1 = 2$ :

$x_2 = \frac{(2)^3}{30} + 2 = \frac{8}{30} + 2 = 0.2667 + 2 = 2.2667$

Thus, $x_2 = 2.2667$ .

Step 2

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Answer

Using the value of $x_2$ to find $x_3$ :

$x_3 = \frac{(x_2)^3}{30} + 2$

Substituting $x_2 = 2.2667$ :

$x_3 = \frac{(2.2667)^3}{30} + 2 = \frac{11.6179}{30} + 2 = 0.3873 + 2 = 2.3873$

Thus, $x_3 = 2.3873$ .

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