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Sample Question 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 \(a_2\)?
\(\textbf{(A) }\ 8 \qquad \textbf{(B) }\ 12 \qquad \textbf{(C) }\ 16 \qquad \textbf{(D) }\ 17 \qquad \textbf{(E) }\ 22\)