3.2. 4 * Find the general term of the sequence $a_{1}=1, a_{2}=2, \frac{a_{n}}{a_{n-1}}=\sqrt{\frac{a_{n-1}}{a_{n-2}}}(n \geqslant 3)$.
From the given, we have
$$
\frac{a_{n}}{a_{n-1}}=\left(\frac{a_{n-1}}{a_{n-2}}\right)^{\frac{1}{2}}=\left(\frac{a_{n-2}}{a_{n-3}}\right)^{\frac{1}{2^{2}}}=\cdots=\left(\frac{a_{2}}{a_{1}}\right)^{\frac{1}{2^{n-2}}},
$$

By changing $n$ to $2,3, \cdots, n$ and multiplying these equations, we get $\frac{a_{n}}{a_{1}}=2^{1+\frac{1}{2}+\cdots+\frac{1}{2^{n-2}}}=2^{2-\left(\frac{1}{2}\right)^{n-2}}$, thus
$$
a_{n}=2^{2-\left(\frac{1}{2}\right)^{n-2}} \text {. }
$$