Solution:

Given that,
The sum of GP $=381$
Where, $a=3, r=6 / 3=2, n=?$
Using the formula,
The sum of GP for $n$ terms $=a\left(r^{n}-1\right) /(r-1)$
$\begin{array}{l}
381=3\left(2^{n}-1\right) /(2-1) \\
381=3\left(2^{n}-1\right) \\
381 / 3=2^{n}-1 \\
127=2^{n}-1 \\
127+1=2^{n} \\
128=2^{n} \\
2^{7}=2^{n} \\
n=7
\end{array}$
Therefore, the value of $n$ is 7