27．（2022•上饶模拟）已知函数f(x)=ax2+bx+c(a>0)f(x)=ax^{2}+bx+c(a>0)f(x)=ax2+bx+c(a>0)有两个零点1和2，若数列{xn}\{x_{n}\}{xn}满足：xn+1=xn−f(xn)f′(xn){x_{n+1}}={x_n}-\frac{f({x_n})}{f'({x_n})}xn+1=xn−f′(xn)f(xn)，记an=lgxn−2xn−1{a_n}=lg\frac{{x_n}-2}{{x_n}-1}an=lgxn−1xn−2，且xn>2x_{n}>2xn>2，a1=3a_{1}=3a1=3，则数列{an}\{a_{n}\}{an}的通项公式an=a_{n}=an=___3⋅2n−1(n∈N+)3\cdot 2^{n-1}(n\in N_{+})3⋅2n−1(n∈N+)___．