25 = a1(1- (0.6)⁴)/(1-0.6)
25 = a1 (1- 0.13)/(0.4)
10 = a1(0.87)
a1 = 11.49
S8 = 11.49(1- (0.6)^8)/(1-0.6)
= 11.49(1-0.017)(1-0.6)
= 11.49(0.983)/0.4
= 28.24
The sum of the first eight terms of the given geometric series is; 28.24
We are told that the sum of the first four terms of the geometric series is 25. Thus, formula for sum of n terms of a geometric series is;
Sₙ = a(1 - rⁿ)/(1 - r)
where;
a is first term
r is common ratio
Thus;
25 = a(1 - (0.6)⁴)/(1 - 0.6)
25 = a(1 - 0.13)/(0.4)
10 = 0.87a
a = 11.49
Thus, sum of the first 8 terms of the series is;
S₈ = 11.49(1 - 0.6⁸)/(1 - 0.6)
S₈ = 11.49(1 - 0.017)(1 - 0.6)
S₈ = 28.24
Read more about Geometric Series at; https://brainly.com/question/24643676
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