(i) The given arrangement, \[2,\text{ }2\surd 2,\text{ }4,\ldots \]
We have,
\[a\text{ }=\text{ }2\text{ }and\text{ }r\text{ }=\text{ }2\surd 2/2\text{ }=\text{ }\surd 2\]
Taking the \[{{n}^{th}}\]term of this arrangement as\[128\], we have
Accordingly, the thirteenth term of the given succession is \[128.\]
(ii) Given arrangement, \[\surd 3,\text{ }3,\text{ }3\surd 3,\ldots \]
We have,
\[a\text{ }=\text{ }\surd 3\text{ }and\text{ }r\text{ }=\text{ }3/\surd 3\text{ }=\text{ }\surd 3\]
Taking the nth term of this arrangement to be \[729,\]we have
Accordingly, the twelfth term of the given succession is \[729.\]