Question

For 0 < a < 4, define the sequence \(\left\{x_n\right\}^{\infin}_{n=1}\) of real numbers as follows :
x₁ = a and x_n+1 + 2 = −x_n(x_n - 4) for n ∈ \(\N\).
Which of the following is/are TRUE ?

• A. \(\left\{x_n\right\}^{\infin}_{n=1}\) converges for at least three distinct values of \(a \in (0,1)\)
• B. \(\left\{x_n\right\}^{\infin}_{n=1}\) converges for at least three distinct values of \(a \in (1,2)\)
• C. \(\left\{x_n\right\}^{\infin}_{n=1}\) converges for at least three distinct values of \(a \in (2,3)\)
• D. \(\left\{x_n\right\}^{\infin}_{n=1}\) converges for at least three distinct values of \(a \in (3,4)\)

Answer 1

The Correct Option is B, C

The correct option is (B) : \(\left\{x_n\right\}^{\infin}_{n=1}\) converges for at least three distinct values of \(a \in (1,2)\) and (C) : \(\left\{x_n\right\}^{\infin}_{n=1}\) converges for at least three distinct values of \(a \in (2,3)\).