Calculate the sum of the first nine terms of a series whose first term is −4 and has a common ratio of −2 .(1 point) Responses −684 negative 684 −2,044 negative 2,044 2,052 2,052 684
To find the sum of the first nine terms of a geometric series, we can use the formula:
S = a * (1 - r^n) / (1 - r)
where:
S = sum of the first n terms
a = first term
r = common ratio
n = number of terms
In this case, a = -4, r = -2, and n = 9.
S = -4 * (1 - (-2)^9) / (1 - (-2))
S = -4 * (1 - 512) / 3
S = -4 * (-511) / 3
S = 2044 / 3
S = 681.333...
Therefore, the sum of the first nine terms of the series is approximately 681.333. The closest response from the given options is 684.