Answer:

Step-by-step explanation:
We have the geometric sequence:
2, 6, 18, 54 ...
And we want to find S8, or the sum of the first eight terms.
The sum of a geometric series is given by:

Where <em>n</em> is the number of terms, <em>a</em> is the first term, and <em>r</em> is the common ratio.
From our sequence, we can see that the first term <em>a</em> is 2.
The common ratio is 3 as each subsequent term is thrice the previous term.
And the number of terms <em>n</em> is 8.
Substitute:

And evaluate. Hence:

The sum of the first eight terms is 6560.