Question

find the sum of the first 8 terms of the following sequence. round to the nearest hundredth if necessary.
24, 144, 864, ...
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 \(24\).
• To find the common ratio \(r\), divide the second term by the first term: \(r=\frac{144}{24} = 6\).
• \(n = 8\) (number of terms).

Step2: Substitute into the formula

Use the formula for the sum of a finite geometric series \(S_n=\frac{a_1(1 - r^n)}{1 - r}\). Substitute \(a_1 = 24\), \(r = 6\), and \(n = 8\):

$$
LATEXBLOCK0
$$

Answer:

\(8062152\)