smc

Using the change of base formula, the three logarithmic terms can be written as $$\frac{\log n}{\log a},\frac{\log n}{\log b},\frac{\log n}{\log c}$$ Since $a$, $b$, and $c$ are members of a geometric sequence, $b=ar$ and $c=a{r}^2$. That means the three logarithmic terms can be rewritten as $$\frac{\log n}{\log a},\frac{\log n}{\log ar},\frac{\log n}{\log a{r}^2}$$ $$\frac{\log n}{\log a},\frac{\log n}{\log a+\log r},\frac{\log n}{\log a+2\log r}$$ Note that if we take the reciprocals of each term, the next term can be derived from the previous term by adding $\frac{\log r}{\log n}$, so the answer is $\boxed{\text{in which the reciprocals of the terms form an A.P}}$.