Question

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)

684

−2,044


−684


2,052

Answer 1

Use the geometric series sum formula S_n = a(1 − r^n)/(1 − r).

Here a = −4, r = −2, n = 9, so r^9 = (−2)^9 = −512.

S_9 = −4(1 − (−512))/(1 − (−2)) = −4(513)/3 = −4·171 = −684.

Answer: −684.