Question

Determine the 5th term of an infinite geometric series if S(infinite)=18 and r=2/3

Answer 1

\[Sum = \frac{a}{1-r}\]
\[18=\frac{a}{1-\frac{2}{3}}\]
\[54=a\]
\[a _{n}=a _{1}r ^{n-1}\]
\[a _{5}=54(\frac{2}{3})^{4}=54(\frac{16}{81})=\frac{32}{3}\]