An iterative formula is shown below.
$x_{n + 1} = \sqrt{8 x_{n} - 5}$
Starting with $x_{1} = 3$ , calculate the values of $x_{2}, x_{3}$ and $x_{4}$ .
Give your answers to 3 d.p.
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$x_{2} \approx 4.359, x_{3} \approx 5.465, x_{4} \approx 6.223$

Steps

Step 1 ：Given the iterative formula: $x_{n + 1} = \sqrt{8 x_{n} - 5}$ and $x_{1} = 3$

Step 2 ：Calculate $x_{2}$ : $x_{2} = \sqrt{8 (3) - 5} = \sqrt{19} \approx 4.359$

Step 3 ：Calculate $x_{3}$ : $x_{3} = \sqrt{8 (4.359) - 5} = \sqrt{29.872} \approx 5.465$

Step 4 ：Calculate $x_{4}$ : $x_{4} = \sqrt{8 (5.465) - 5} = \sqrt{38.720} \approx 6.223$

Step 5 ： $x_{2} \approx 4.359, x_{3} \approx 5.465, x_{4} \approx 6.223$