Respuesta :

sharmaenderp
Observe that as the series progresses, the term decreases by 1/4. To show this, observe the first four terms of the series below.

-200 = (1/4)(-800)
-50 = (1/4)(-200)
-12.5 = (1/4)(-50)

Since we have a common ratio, r, of 1/4, we can use the properties of a geometric series to find the 8th term of the series.

Recall that to find the sum of the nth term of a geometric series, we have

[tex] S_{n} = a(\frac{1-r^{n}}{1-r}) [/tex]

where a is the first term of the series and r is the ratio.

So, for the first eight terms, we have

[tex] S_{8} = -800(\frac{1-(\frac{1}{4})^8}{1- \frac{1}{4}}) [/tex]
[tex] S_{8} \approx -1066.65 [/tex]

Therefore, the sum of the 8th series is approximately -1066.65. 

Answer: -1066.65

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