2008 AMC12 A #16

The numbers $\log \left ( a^3 b^7 \right ) , \log \left ( a^5 b^{12} \right )$, and $\log \left ( a^8 b^{15} \right )$ are the first three terms of an arithmetic sequence, and the $12^{th}$ term of the sequence is $\log \left ( b^n \right )$. What is $n$ ?

(A) $40$          (B) $56$         (C) $76$          (D) $112$          (E) $143$

정답 (D)