Final answer:
None of the options provided for the values of x1, x2, x3, and x4 in the sequence match the calculated values obtained by applying the given iterative formula. The calculated values are x1 ≈ 3.3166, x2 ≈ 3.8660, x3 ≈ 4.0743, x4 ≈ 4.1494. A double-check of both calculations and the provided options is needed to ensure accuracy.
Step-by-step explanation:
To find the values of x1, x2, x3, and x4 in the sequence given by the iterative formula x_{n+1} = √(3x_n + 5), with the initial value of x_0 = 2, we plug in the known values into the formula and calculate each term step by step.
- x1 = √(3×2 + 5) = √(6 + 5) = √11 ≈ 3.3166
- x2 = √(3×3.3166 + 5) = √(9.9498 + 5) = √14.9498 ≈ 3.8660
- x3 = √(3×3.8660 + 5) = √(11.598 + 5) = √16.598 ≈ 4.0743
- x4 = √(3×4.0743 + 5) = √(12.2229 + 5) = √17.2229 ≈ 4.1494
However, comparing these calculated values with the options provided, none of the options match. Therefore, there might be a mistake in the question's options or perhaps in the calculations. Make sure to double-check the calculations and the question for accuracy.