Question

The sequence $\log \,a$, $\log \frac{a^{2}}{b}, \,\log \frac{a^{3}}{b^{2}}, ...........$ is

• A. a G.P.
• B. an A.P.
• C. a H.P.
• D. both a G.P. and a H.P

Answer 1

Answer: (B)

an A.P.

Answer 2

Let $S=\log a, \log \frac{a^{2}}{b}, \log \frac{a^{3}}{b^{2}}, \ldots$ $=\log a,(2 \log a-\log b) (3 \log a-2 \log b)$, Now, $T_{2}-T_{1}=\log a-\log b$ and $T_{3}-T_{2}=\log a-\log b$ Hence, it is an AP.