Answer:
(i) and (ii)
Step-by-step explanation:
For a sequence to be geometric then the ratio r between consecutive terms must be common.
(1)
2, 6, 18, 54
6 ÷ 2 = 3
18 ÷ 6 = 3
54 ÷ 18 = 3
Here there is a common ratio r = 3 , then sequence is geometric
(ii)
25, 5, 1
[tex]\frac{5}{25}[/tex] = [tex]\frac{1}{5}[/tex] and [tex]\frac{a_{3} }{a_{2} }[/tex] = [tex]\frac{1}{5}[/tex]
There is a common ratio r = [tex]\frac{1}{5}[/tex] , then sequence is geometric
(iii)
1, 4, 9, 16
4 ÷ 1 = 4
9 ÷ 4 = 2.25
16 ÷ 9 = 1.777..
There is no common ratio, then sequence is not geometric
