Question

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

Answer 1

(i) and (ii)

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

`(5)/(25)` =
`(1)/(5)` and
`(a_(3) )/(a_(2) )` =
`(1)/(5)`

There is a common ratio r =
`(1)/(5)` , 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