Solution:
(i) $2,6,18, \ldots$ to 7 terms
It is known that, the sum of GP for $n$ terms $=a\left(r^{n}-1\right) /(r-1)$
Given that,
$a=2, r=t_{2} / t_{1}=6 / 2=3, n=7$
Substitute the values in
$\begin{array}{l}
\mathrm{a}\left(r^{\mathrm{n}}-1\right) /(\mathrm{r}-1)=2\left(3^{7}-1\right) /(3-1) \\
=2\left(3^{7}-1\right) / 2 \\
=3^{7}-1 \\
=2187-1 \\
=2186
\end{array}$
(ii) $1,3,9,27, \ldots$ to 8 terms
It is known that, the sum of GP for $n$ terms $=a\left(r^{n}-1\right) /(r-1)$
Given that,
$a=1, r=t_{2} / t_{1}=3 / 1=3, n=8$
Substitute the values in
$\begin{array}{l}
\mathrm{a}\left(r^{\mathrm{n}}-1\right) /(\mathrm{r}-1)=1\left(3^{8}-1\right) /(3-1) \\
=\left(3^{8}-1\right) / 2 \\
=(6561-1) / 2 \\
=6560 / 2 \\
=3280
\end{array}$