Show that the sequence `loga ,log(a b),log(a b^2),log(a b^3),` is an A.P. Find its nth term.

Explanation

To show that the sequence \( \log a, \log(ab), \log(ab^2), \log(ab^3) \) is an arithmetic progression (A.P.) and to find its \( n \)-th term, we can follow these steps:

### Step 1: Identify the terms of the sequence
The given sequence consists of the following terms:
1. \( a_1 = \log a \)
2. \( a_2 = \log(ab) \)
3. \( a_3 = \log(ab^2) \)
4. \( a_4 = \log(ab^3) \)
...