Question

Y’all mind helping thanks much love :) look at the picture

Answer 1

`S_8= 191.997071\approx 192`

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:
`S_8`

`\huge \because S_n= (a(1-r^n))/(1-r)`

`\huge \therefore S_8= (144[1-(0.25)^8])/(1-0.25)`

`\therefore S_8= (144[1-0.00001525878])/(0.75)`

`\therefore S_8= (144[0.999984741])/(0.75)`

`\huge \therefore S_8= (143.997802734)/(0.75)`

`\huge \therefore S_8= 191.997071`