Final answer:
The values of x₂, x₃, and x₄ in the iterative sequence starting with x₁ = 2 are 1.5, 1.125, and 0.84375 respectively, found by multiplying each preceding term by three-quarters.
Step-by-step explanation:
The iterative formula given is X₍n+1₎ = ¾X₍n−1₎, and we are asked to find the values of x₂, x₃, and x₄, given that x₁ = 2. Since the formula states that each term in the sequence is three-quarters of the previous term, we can work this out step by step:
- x₂ = ¾ × x₁ = ¾ × 2 = 1.5
- x₃ = ¾ × x₂ = ¾ × 1.5 = 1.125
- x₄ = ¾ × x₃ = ¾ × 1.125 = 0.84375
Therefore, the values required are x₂ = 1.5, x₃ = 1.125, and x₄ = 0.84375.