Answer :
Final answer:
The sum of the first six terms of the geometric series is -364.
Explanation:
To find the sum of the first six terms of the geometric series, we can use the formula for the sum of a geometric series. The formula is given by:
- Sum = (first term) * (1 - (common ratio)^(number of terms)) / (1 - (common ratio))
In this case, the first term is 2 and the common ratio is -3. Plugging in these values into the formula, we get:
- Sum = 2 * (1 - (-3)^6) / (1 - (-3))
- Sum = 2 * (1 - 729) / (1 + 3)
- Sum = 2 * (-728) / 4
- Sum = -364
Therefore, the sum of the first six terms of the geometric series is -364, which corresponds to option (a).
