Answer
\[3,\,\,6,\,\,12,\,\,24,\,\,48,\ \text{and}\ 96\].
Work Step by Step
For the second term put \[n=2\] in the general formulae stated above.
\[\begin{align}
& {{a}_{2}}={{a}_{1}}{{r}^{2-1}} \\
& =3\cdot {{2}^{1}} \\
& =3\cdot 2 \\
& =6
\end{align}\]
For the third term put \[n=3\] in the general formula stated above.
\[\begin{align}
& {{a}_{3}}={{a}_{1}}{{r}^{3-1}} \\
& =3\cdot {{2}^{2}} \\
& =3\cdot 4 \\
& =12
\end{align}\]
For the fourth term put \[n=4\] in the general formulae stated above.
\[\begin{align}
& {{a}_{4}}={{a}_{1}}{{r}^{4-1}} \\
& =3\cdot {{2}^{3}} \\
& =3\cdot 8 \\
& =24
\end{align}\]
For the fifth term put \[n=5\] in the general formulae stated above.
\[\begin{align}
& {{a}_{5}}={{a}_{1}}{{r}^{5-1}} \\
& =3\cdot {{2}^{4}} \\
& =3\cdot 16 \\
& =48
\end{align}\]
For the sixth term put \[n=6\] in the general formulae stated above.
\[\begin{align}
& {{a}_{6}}={{a}_{1}}{{r}^{6-1}} \\
& =3\cdot {{2}^{5}} \\
& =3\cdot 32 \\
& =96
\end{align}\]
The first six terms of the geometric sequence are \[3,\,\,6,\,\,12,\,\,24,\,\,48,\ \text{and}\ 96\].
