Question

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

Answer 1

Answer:

$S_8= 191.997071\approx 192$

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: $S_8$

$\huge \because S_n= \frac{a(1-r^n)}{1-r}$

$\huge \therefore S_8= \frac{144[1-(0.25)^8]}{1-0.25}$

$\therefore S_8= \frac{144[1-0.00001525878]}{0.75}$

$\therefore S_8= \frac{144[0.999984741]}{0.75}$

$\huge \therefore S_8= \frac{143.997802734}{0.75}$

$\huge \therefore S_8= 191.997071$