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.
$< $ Back
Watch video
Answer

Answer

Expert–verified

Hide Steps

Answer

$\boxed{x_2 \approx 4.359, x_3 \approx 5.465, x_4 \approx 6.223}$

Steps

Step 1 ：Given the iterative formula: $x_{n+1} = \sqrt{8x_n - 5}$ 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 ：$\boxed{x_2 \approx 4.359, x_3 \approx 5.465, x_4 \approx 6.223}$