Answer
(i) The sequence is geometric.
(ii) The next two terms are: $25\sqrt5$ and $125$.
Work Step by Step
A sequence is:
(a) arithmetic if there is a common difference among the terms.
(b) geometric if there is a common ratio among the terms.
Notice that in the given sequence:
$5 \div \sqrt5 = \sqrt5
\\5\sqrt5 \div 5 = \sqrt5$
This means that the sequence has a common ratio of $\sqrt5$.
Thus, the sequence is $\underline{\text{geometric}}$.
The next two terms can be found by multiplying $\sqrt5$ to the previous term.
Therefore, the next two terms are:
$25 \times \sqrt5 = 25\sqrt5
\\25\sqrt5 \times \sqrt5 = 25(5) = 125$
