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

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 ：\(\boxed{x_2 \approx 4.359, x_3 \approx 5.465, x_4 \approx 6.223}\)