Question

find the sum of the first 8 terms of the following sequence. round to the nearest hundredth if necessary.
20, 8, \\(\frac{16}{5}\\),…
sum of a finite geometric series:
\\(s_n = \frac{a_1 (1 - r^n)}{1 - r}\\)

Explanation:

Step1: Identify \(a_1\), \(r\), and \(n\)

• \(a_1\) (first term) is \(20\).
• To find the common ratio \(r\), divide the second term by the first term: \(r=\frac{8}{20}=\frac{2}{5} = 0.4\).
• \(n = 8\) (number of terms).

Step2: Substitute into the geometric series sum formula

The formula for the sum of the first \(n\) terms of a geometric series is \(S_n=\frac{a_1(1 - r^n)}{1 - r}\).
Substitute \(a_1 = 20\), \(r = 0.4\), and \(n = 8\) into the formula:

$$
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$$

Answer:

\(33.31\) (rounded to the nearest hundredth)