2. Given the sequence $\left\{a_{n}\right\}$ consists of positive integers and is an increasing sequence, and satisfies $a_{n+2}=a_{n+1}+2 a_{n}\left(n \in \mathbf{N}_{+}\right)$. If $a_{5}$ $=52$, then $a_{7}=(\quad)$.
(A) 102
(B) 152
(C) 212
(D) Insufficient conditions, $a_{7}$ cannot be uniquely determined
2.C.
$$
\begin{array}{l}
a_{3}=a_{2}+2 a_{1}, \\
a_{4}=a_{3}+2 a_{2}=3 a_{2}+2 a_{1}, \\
a_{5}=a_{4}+2 a_{3}=5 a_{2}+6 a_{1} .
\end{array}
$$

The positive integer solutions to the equation $5 a_{2}+6 a_{1}=52$ are $a_{1}=2, a_{2}=8$ or $a_{1}=7, a_{2}=2$.
Since $a_{2}>a_{1}$, we have $a_{1}=2, a_{2}=8$.
Thus, $a_{7}=a_{6}+2 a_{5}=21 a_{2}+22 a_{1}=212$.