AMC 12B 2022 Problem 9

The sequence a_{0}, a_{1}, a_{2}, \cdots is a strictly increasing arithmetic sequence of positive integers such that

2^{a_{7}}=2^{27} \cdot a_{7}

What is the minimum possible value of a_{2} ?

Answer Choices
A. 8
B. 12
C. 16
D. 17
E. 22