3. "The three numbers $\lg x, \lg y, \lg z$ form an arithmetic sequence" is a () condition for "$y^{2}=x z$".
(A) Sufficient but not necessary
(B) Necessary but not sufficient
(C) Sufficient and necessary
(D) Neither sufficient nor necessary
3. A.

From the problem, we know
$$
\begin{array}{l}
2 \lg y=\lg x+\lg z \\
\Rightarrow \lg y^{2}=\lg x z \Rightarrow y^{2}=x z .
\end{array}
$$

However, the converse is not necessarily true. When $x, y, z=0$, it is meaningless.