Determine the number of terms in G.P. `ifa_1=3,a_n=96 and S_n=189.`

Explanation

To determine the number of terms in the geometric progression (G.P.) given that \( a_1 = 3 \), \( a_n = 96 \), and \( S_n = 189 \), we can follow these steps:

### Step 1: Use the formula for the nth term of a G.P.
The nth term of a G.P. is given by the formula:
\[ a_n = a_1 \cdot r^{n-1} \]
Substituting the known values:
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