已知数列 {an}\left\{ {a}_{n}\right\}{an} 满足, a1=3,anan+1=9×22n−1,n∈N∗{a}_{1} = 3,{a}_{n}{a}_{n + 1} = 9 \times {2}^{{2n} - 1},n \in {\mathrm{N}}^{ * }a1=3,anan+1=9×22n−1,n∈N∗ .（1）求数列 {an}\left\{ {a}_{n}\right\}{an} 的通项公式；（2）证明：数列 {an}\left\{ {a}_{n}\right\}{an} 中的任意三项均不能构成等差数列.