3. Given that the terms of the arithmetic sequence $\left\{a_{n}\right\}$ and the geometric sequence $\left\{b_{n}\right\}$ are all positive, and $a_{1}=b_{1}, a_{2 n+1}=b_{2 n+1}$. Then, it must be true that ( ).
(A) $a_{n+1}b_{n+1}$
(D) $a_{n+1} \geqslant b_{n+1}$
3.D.
$$
a_{n+1}=\frac{a_{1}+a_{2 n+1}}{2}=\frac{b_{1}+b_{2 n+1}}{2} \geqslant \sqrt{b_{1} b_{2 n+1}}=b_{n+1} \text{. }
$$