Question 6
Let $\{x_n\}$ be the real sequence defined by
$$x_1=a,\qquad x_{n+1}=3x_n^3-7x_n^2+5x_n\quad(n\in\mathbb N).$$
Determine all real $a$ for which the sequence has a finite limit as $n\to+\infty$, and determine the limit in each case.
$$x_1=a,\qquad x_{n+1}=3x_n^3-7x_n^2+5x_n\quad(n\in\mathbb N).$$
Determine all real $a$ for which the sequence has a finite limit as $n\to+\infty$, and determine the limit in each case.