Question

Please help meee oh please

Answer 1

Collecting the data of this P.G., comes:

The 1st term $a_{1} = 648$
The 2nd term $a_{2} = 216$
 
The ratio $r = \frac {a2}{a1}$
The number of terms n = 8
 
The 8th term $a_{8} = ?$

The value of ratio, we have:
The ratio $r = \frac {a2}{a1}$
$r = \frac {a2}{a1} = \frac{216}{648} \frac{\div6}{\div6} = \frac{36}{108} \frac{\div6}{\div6} = \frac{6}{18} \frac{\div6}{\div6} \to\:r= \frac{1}{3}$

Applying the general term formula of P.G., comes:
$a_{n} = a_{1} *r^{n-1}$
$a_{8} = 648 * (\frac{1}{3}) ^{8-1}$
$a_{8} = 648 * (\frac{1}{3}) ^{7}$
$a_{8} = 648 * \frac{1}{3^7}$
$a_{8} = 648 * \frac{1}{2187}$
$a_{8} = \frac{648}{2187}$
Simplify

$a_{8} = \frac{648}{2187} \frac{\div9}{\div9} = \frac{72}{243} \frac{\div9}{\div9} \to\: \boxed{\boxed{a_{8} = \frac{8}{27}}}\end{array}}\qquad\quad\checkmark$

Answer:
$\boxed{\boxed{a_{8} = \frac{8}{27}}}$