8
QuizMultiple Choice

Sequences and Iteration

Question 8 • TX-Advanced Quantitative Reasoning

Find the first four iterates of the function f(x) = (x - 5)2 with an initial value of x0 = 4.

Answer
A
4; 19; 645; 12,645
B
1; 16; 121; 13,456
C
1; 19; 645; 12,645
D
4; 16; 121; 13,456

Explanation

Apply f(x) = (x − 5)² repeatedly, starting with x₀ = 4. The first value is x₁ = (4 − 5)² = 1; then x₂ = (1 − 5)² = 16, x₃ = (16 − 5)² = 121, and x₄ = (121 − 5)² = 13,456. So the correct choice is B: 1; 16; 121; 13,456.

AI-written and checked against the verified answer.

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