Math Gold Medalist

Lor

2022 AMC 12B 

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 $a_2$?

$\textbf{(A) }\ 8 \qquad \textbf{(B) }\ 12 \qquad \textbf{(C) }\ 16 \qquad \textbf{(D) }\ 17 \qquad \textbf{(E) }\ 22$

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   Solution