How many terms of G.P. `3,3^2,3^3,dotdotdot`are needed to give the sum 120?

Explanation

To find out how many terms of the geometric progression (G.P.) \(3, 3^2, 3^3, \ldots\) are needed to give the sum of 120, we can follow these steps:

### Step 1: Identify the first term and common ratio
The first term \(a\) of the G.P. is \(3\) and the common ratio \(r\) is also \(3\).

### Step 2: Write the formula for the sum of the first \(n\) terms of a G.P.
The sum \(S_n\) of the first \(n\) terms of a G.P. can be calculated using the formula:
\[
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