Mathematics · Real Analysis
Let f : &mathbb;R → &mathbb;R be defined as f(x) = 14 + x − x2. Given a ∈ &mathbb;R, let us define the sequence {xn} by x0 = a and xn = f(xn−1) for n ≥ 1. Which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1If a = 0, then the sequence {xn} does not converge.
- 2The sequence {xn} converges for every a ∈ (−12, 32), and it converges to 12.
- 3If a = 0, then the sequence {xn} converges to −12.
- 4If a = 0, then the sequence {xn} converges to 12.✓
Correct answer
If a = 0, then the sequence {xn} converges to 12.
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