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^{\text {th }} term of the sequence is \log \left(b^{n}\right). What is n ?
Answer Choices
A. 40
B. 56
C. 76
D. 112
E. 143