Respuesta :
Answer:
-1066.65 to 2 decimal places.
Step-by-step explanation:
(−800)+(−200)+(−50)+(−12.5)+...
This is a Geometric series with common ratio r =(-200) / ) / (-800) = 0.25 and first term a1 = -800.
Sum of n terms = a1 * (1 - r^n) / (1 - r)
Sum of 8 terms = -800 * (1 - 0.25^8) / (1 - 0.25)
= -800 * 1.333313
= -1066.65.
The sum of the first eight terms of the geometric sequence is given by: −1066.65
What is a geometric sequence?
A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
The sum of the first n terms is given by:
[tex]S_n = \frac{a_1(r^n - 1)}{r - 1}[/tex]
In this problem, we have that the first term and the common ratio are, respectively:
[tex]a_1 = -800, q = \frac{-200}{-800} = 0.25[/tex]
Hence, the sum of the first eight terms is given by:
[tex]S_n = \frac{-800(0.25^8 - 1)}{0.25 - 1 } = −1066.65[/tex]
More can be learned about geometric sequences at https://brainly.com/question/11847927
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