(i) Given arrangement:\[~8,\text{ }24,\text{ }72,\text{ }216,\text{ }\ldots \text{ }\ldots \]

Since,

\[24/8\text{ }=\text{ }3,\text{ }72/24\text{ }=\text{ }3,\text{ }216/72\text{ }=\text{ }3\]

\[\Rightarrow 24/8\text{ }=\text{ }72/24\text{ }=\text{ }216/72\text{ }=\ldots \ldots ..\text{ }=\text{ }3\]

Along these lines \[8,\text{ }24,\text{ }72,\text{ }216,\text{ }\ldots \text{ }\ldots \]is a G.P. with a typical proportion \[3.\]

(ii) Given arrangement: \[1/8,\text{ }1/24,\text{ }1/72,\text{ }1/216,\text{ }\ldots \ldots \]

Since,

\[\left( 1/24 \right)/\left( 1/8 \right)\text{ }=\text{ }1/3,\text{ }\left( 1/72 \right)/\left( 1/24 \right)\text{ }=\text{ }1/3,\text{ }\left( 1/216 \right)/\left( 1/72 \right)\text{ }=\text{ }1/3\]

\[\Rightarrow \left( 1/24 \right)/\left( 1/8 \right)\text{ }=\text{ }\left( 1/72 \right)/\left( 1/24 \right)\text{ }=\text{ }\left( 1/216 \right)/\left( 1/72 \right)\text{ }=\ldots \ldots ..\text{ }=\text{ }1/3\]

Along these lines \[1/8,\text{ }1/24,\text{ }1/72,\text{ }1/216,\text{ }\ldots \ldots \,\] is a G.P. with a typical proportion \[1/3.\]