Final answer:
The sum of the first 11 terms of the given geometric sequence is -531,440.
Step-by-step explanation:
To find the sum of the first 11 terms of a geometric sequence, we can use the formula:
Sum = first term * (1 - r^n) / (1 - r),
where the first term is 6 and the common ratio is 3.
Plugging these values into the formula, we get:
Sum = 6 * (1 - 3^11) / (1 - 3) = 6 * (1 - 177147) / -2 = -531,440.