Question

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

• A. a GP
• B. an AP
• C. a HP
• D. both a GP and a HP

Answer 1

Answer: (B)

an AP

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

Lets see the common difference between consecutive terms.

$\log \frac{a^2}{b^2}-\log \frac{a}{b}=\log \frac{a}{b}$, $\log \frac{a^3}{b^3}-\log \frac{a^2}{b^2}=\log \frac{a}{b}$

Its difference is same. Thus it is an A.P.

It is an AP with general term $t_n=n\log \frac{a}{b}$

So, option B is correct.