According to the given question,

G.P: \[3,\text{ }6,\text{ }12,\text{ }\ldots .,\text{ }1536\]

So,

\[a\text{ }=\text{ }3,\text{ }l\text{ }=\text{ }1536\] and \[r\text{ }=\text{ }6/3\text{ }=\text{ }2\]

So,

The sum of terms \[=\text{ }\left( lr\text{ }-\text{ }a \right)/\text{ }\left( r\text{ }-\text{ }1 \right)\]

\[=\text{ }\left( 1536\text{ }x\text{ }2\text{ }-\text{ }3 \right)/\text{ }\left( 2\text{ }-\text{ }1 \right)\]

\[=\text{ }3072\text{ }-\text{ }3\]

\[=\text{ }3069\]