Collecting the data of this P.G., comes:
The 1st term [tex] a_{1} = 648[/tex]
The 2nd term [tex] a_{2} = 216[/tex]
The ratio [tex]r = \frac {a2}{a1}
[/tex]
The number of terms n = 8
The 8th term [tex] a_{8} = ?[/tex]
The value of ratio, we have:
The ratio [tex]r = \frac {a2}{a1} [/tex]
[tex]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} [/tex]
Applying the general term formula of P.G., comes:
[tex] a_{n} = a_{1} *r^{n-1}[/tex]
[tex]a_{8} = 648 * (\frac{1}{3}) ^{8-1}[/tex]
[tex]a_{8} = 648 * (\frac{1}{3}) ^{7}[/tex]
[tex]a_{8} = 648 * \frac{1}{3^7} [/tex]
[tex]a_{8} = 648 * \frac{1}{2187}[/tex]
[tex]a_{8} = \frac{648}{2187} [/tex]
Simplify
[tex]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 [/tex]
Answer:
[tex]\boxed{\boxed{a_{8} = \frac{8}{27}}}[/tex]
