(3) "The three numbers $\lg x, \lg y, \lg z$ form an arithmetic sequence" is ( ) for " $y^{2}=x z$ " to hold.
(A) A sufficient but not necessary condition
(B) A necessary but not sufficient condition
(C) A necessary and sufficient condition
(D) Neither a sufficient nor a necessary condition
(3) A Hint: If $\lg x, \lg y, \lg z$ form an arithmetic sequence, then $2 \lg y = \lg x + \lg z$, so $\lg y^{2} = \lg (x z)$. Therefore, $y^{2} = x z$, but not conversely, for example, if $x, y, z$ are 0, the logarithm is undefined.