Question

What is the sum of the first six terms of the geometric series? 2 - 6 + 18 - 54 + … a. -364 b. 364

c. 182
d. -182

Answer 1

The sum of the first six terms of the geometric series is -364.

Step-by-step 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).