Question

What is the common ratio between successive terms in the sequence?

27, 9, 3, 1, 1/3,1/9,1/27,....​

Answer 1

r =
`(1)/(3)`

Explanation:

The ratio between successive terms is

`(9)/(27)` =
`(1)/(3)`

`(3)/(9)` =
`(1)/(3)`

`(1)/(3)`

`((1)/(3) )/(1)` =
`(1)/(3)`

`((1)/(9) )/((1)/(3) )` =
`(1)/(3)`

`((1)/(27) )/((1)/(9) )` =
`(1)/(3)`

Since the common ratio between terms is constant then sequence is geometric

Answer 2

It's 1/3.

Explanation:

Common ratio = 9/27 = 1/3.

3 / 9 = 1/3

1 / 3 = 1/3 and so on.