Q4) Identify which of the following are geometric sequences and which are not
(i) 2, 6, 18, 54
(ii) 25,5, 1,
(iii) 1, 4, 9, 16

(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

= and =

There is a common ratio r = , 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

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