2. Let the arithmetic sequence $\left\{a_{n}\right\}$ and the geometric sequence $\left\{b_{n}\right\}$ satisfy $0b_{3}$, (3) $a_{6}>b_{6}$, (4) $a_{5}<b_{6}$, the number of correct statements is $($ ) .
(A) 0
(B) 1
(C) 2
(D) 3
2. B.

Notice,
$$
a_{3}=\frac{a_{1}+a_{5}}{2}=\frac{b_{1}+b_{5}}{2}>\sqrt{b_{1} b_{5}}=b_{3},
$$

thus, conclusion (2) is correct, and conclusion (1) is incorrect.
$$
\text { Let } a_{n}=1+20(n-1) \text {. }
$$

If we take $b_{n}=3^{n-1}$, we know $a_{6}b_{6}$, thus, conclusion (4) is incorrect.