Question

what is the common ratio between successive terms in the sequence? 27, 9, 3, 1, 1/3, 1/9, 1,27,.... 3 1/3 3

Answer 1

The common ratio is;

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

Answer 2

Option 2nd is correct

common ratio between successive terms in the sequence is
`(1)/(3)`

Explanation:

Common ratio(r) defined as the ratio of a term to the previous term.

Also, this common ratio term is constant.

Given the sequence:

27, 9, 3, 1, 1/3, 1/9, 1/27,....

⇒
`a_1 = 27`

`a_2 = 9`

`a_3 = 3` ......

Then by definition of common ratio:

`r = (a_2)/(a_1)=(a_3)/(a_2)....`

Substitute the given values we have;

`r = (9)/(27) = (3)/(9)....`

⇒
`r = (1)/(3)`

Therefore, the common ratio between successive terms in the sequence is
`(1)/(3)`