Answer
The sum of the first six terms $\left( {{S}_{6}} \right)$ of the sequence, $3,6,9,12,\ldots $ is$63$.
Work Step by Step
$3,6,9,12,\ldots $
So, the expansion of the sequence is,
${{a}_{n}}=3n$,
For, ${{S}_{6}}$
The sum of the first $6$ terms of the sequence is given by,
$\begin{align}
& {{S}_{6}}=3+6+9+12+15+18 \\
& =9+9+12+33 \\
& =63
\end{align}$.
Thus, the sum of the first six terms $\left( {{S}_{6}} \right)$ of the sequence $3,6,9,12,\ldots $ is $63$.
