2. In the positive term sequence $\left\{a_{n}\right\}$, $a_{1}=10, a_{n+1}=10 \sqrt{a_{n}}$, find the general formula for this sequence.
2. Given $a_{1}>0, a_{n+1}=10 \sqrt{a_{n}}$, taking the logarithm on both sides, we get $\lg a_{n+1}=1+\frac{1}{2} \lg a_{n}$. Let $x_{n}=\lg a_{n}$, then $x_{n+1}=\frac{1}{2} x_{n}+1$, $x_{n}=\frac{1}{2} x_{n-1}+1$. Subtracting the two equations, we get $x_{n+1}-x_{n}=\frac{1}{2}\left(x_{n}-x_{n-1}\right)$, and $x_{2}-x_{1}=\frac{1}{2}$. Therefore, $x_{n+1}=x_{1}+\sum_{k=1}^{n}\left(x_{k+1}-\right.$ $\left.x_{k}\right)=1+1-\left(\frac{1}{2}\right)^{n}=2-\left(\frac{1}{2}\right)^{n}$. Hence, $a_{n}=10^{2-\left(\frac{1}{2}\right)^{n-1}}$.