Question 21
Suppose sequence $\{a_n\}$ satisfies $a_1 = 2t - 3$ ($t \in \mathbb{R}$ and $t \neq \pm 1$),
$$
a_{n+1} = \frac{(2t^{n+1} - 3)a_n + 2(t-1)t^n - 1}{a_n + 2t^n - 1} \quad (n \in \mathbb{N}^*).
$$
(1)
Find the formula of general term about $\{a_n\}$.
(2)
If $t \gt 0$, find out which is larger between $a_{n+1}$ and $a_n$.
$$
a_{n+1} = \frac{(2t^{n+1} - 3)a_n + 2(t-1)t^n - 1}{a_n + 2t^n - 1} \quad (n \in \mathbb{N}^*).
$$
(1)
Find the formula of general term about $\{a_n\}$.
(2)
If $t \gt 0$, find out which is larger between $a_{n+1}$ and $a_n$.