The sum of the first nth terms of a geometric sequence is given by:
[tex]S_n=\frac{a(1-r^n)}{1-r}[/tex]
where a is the first term and r is the common ratio.
We know the geometric series is given by:
[tex]a_n=3(2)\placeholder{⬚}^{n-1}[/tex]
which means that the first term is 3 and the common ratio is 2. Since we want to know the sum of the first nth terms this means that n=10; plugging these values in the expression for the sum we have:
[tex]\begin{gathered} S_{10}=\frac{3(1-2^{10})}{1-2} \\ S_{10}=3069 \end{gathered}[/tex]
Therefore, the sum we are looking for is 3069
