Answer:
[tex] S_8= 191.997071\approx 192[/tex]
Step-by-step explanation:
Given series is: 144, 36, 9,...
Here. 36/144 = 1/4, 9/36 = 1/4
Since, the ratio any two consecutive terms is same.
Therefore, it is a geometric progression.
So,
Common ratio (r) = 1/4= 0.25
First term (a) = 144
n = 8
To find: [tex] S_8[/tex]
[tex] \huge \because S_n= \frac{a(1-r^n)}{1-r}[/tex]
[tex] \huge \therefore S_8= \frac{144[1-(0.25)^8]}{1-0.25}[/tex]
[tex] \therefore S_8= \frac{144[1-0.00001525878]}{0.75}[/tex]
[tex] \therefore S_8= \frac{144[0.999984741]}{0.75}[/tex]
[tex]\huge \therefore S_8= \frac{143.997802734}{0.75}[/tex]
[tex]\huge \therefore S_8= 191.997071[/tex]
