Answer:
S_n = 99.18
Step-by-step explanation:
The series is;
200, -160, 128...
Now,the common ration would be gotten by dividing two consecutive terms i.e. a2/a1, a3/a2, a4/a3 e.t.c.
Now,
r = -160/200
r = -4/5
Formula for sum of geometric series is;
S_n = a1(1 - rⁿ)/(1 - r)
Where a1 is the first term and n is the number of terms in the series.
In this case;
a1 = 200
n = 10
Thus;
S_n = 200(1 - (-4/5)^(10))/(1 - (-4/5))
S_n = 99.18
