Question

Find the sum of the first 10 terms of the following sequence. Round to the nearest

hundredth if necessary.
200,
-160,
128,...

Answer 1

S_n = 99.18

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