2, 3, 3, 5, 10, 13, ?, 43, 172, 177

The answer is $\boxed{38}$.

The sequence is generated by the following formula:

$a_n = \begin{cases} 2 & \text{if } n = 1 \\ 3 + (n – 1) \cdot 2 & \text{if } n > 1 \end{cases}$

In other words, the first term is 2, and each subsequent term is 2 more than the previous term.

Therefore, the seventh term is $3 + (7 – 1) \cdot 2 = 38$.

Option A, 23, is incorrect because it is not generated by the given formula.

Option B, 38, is correct because it is generated by the given formula.

Option C, 39, is incorrect because it is not generated by the given formula.

Option D, 40, is incorrect because it is not generated by the given formula.