How many terms of the G.P. `3`, `3/2`,`3/4`are needed to give the sum `(3069)/(512)`?

Explanation

To solve the problem, we need to determine how many terms of the geometric progression (G.P.) \(3, \frac{3}{2}, \frac{3}{4}\) are required to achieve a sum of \(\frac{3069}{512}\).

### Step-by-Step Solution:

1. **Identify the first term (A) and the common ratio (R)**:
- The first term \(A = 3\).
- The second term is \(\frac{3}{2}\), and the third term is \(\frac{3}{4}\).
- To find the common ratio \(R\), we can calculate:
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