. According to the given question,

G.P: \[2\text{ }+\text{ }6\text{ }+\text{ }18\text{ }+\text{ }\ldots ..\]

Here,

\[a\text{ }=\text{ }2\]

And

\[r\text{ }=\text{ }6/2\text{ }=\text{ }3\]

Also given,

\[{{S}_{n}}~=\text{ }728\]

\[{{S}_{n}}~=\text{ }a({{r}^{n~}}-\text{ }1)/\text{ }r\text{ }-\text{ }1\]

\[728\text{ }=\text{ }\left( 2 \right)({{3}^{n~}}-\text{ }1)/\text{ }3\text{ }-\text{ }1=\text{ }{{3}^{n~}}-\text{ }1\]

\[729\text{ }=\text{ }{{3}^{n}}\]

\[{{3}^{6}}~=\text{ }{{3}^{n}}\]

\[n\text{ }=\text{ }6\]

Hence, \[6\text{ }terms\]must be taken to make the sum equal to\[728\].