Question

Which of the following could be used to calculate the sum of the first eight terms of the sequence whose first three terms are 6400, 800, 100, ... ?(1 point)

S6400=6400(1−(8)8)1−8


S8=8(1−(6400)18)1−6400


S8=6400(1−(18)8)1−18


S6400=8(1−(18)6400)1−18

Answer 1

The sequence is geometric with a1 = 6400 and r = 800/6400 = 1/8. Use the geometric sum formula S_n = a1(1 − r^n)/(1 − r). For n = 8 that gives

S8 = 6400(1 − (1/8)^8)/(1 − 1/8),

which is the third option.