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:
\(\boxed{\boxed{a_{8} = \frac{8}{27}}}\)
