Question

Which formula can be used to describe the sequence below?

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

- an = -3an-1;a1=27

- an=1/3an-1;a1=27

- an=an-1-3;a1=27

- an=3an-1-1/3;a1=27

Answer 1

`a_n` =
`(1)/(3)`
`a_n_-_1` ;
`a_1` =27 is the correct equation

Explanation:

For the sequence : 27,9,3,1,1/3, ....

Lets check all the given equations:

->
`a_n` = -3
`a_n_-_1` ;
`a_1` =27

`a_2` = -3(
`a_1` )= -3(27)=> -81 (this equation doesn't satisfy the sequence)

->
`a_n` =
`(1)/(3)`
`a_n_-_1` ;
`a_1` =27

`a_2` =
`(1)/(3)`
`a_1` =
`(1)/(3)` (27) => 9

`a_3` =
`(1)/(3)`
`a_2` =
`(1)/(3)` (9) => 3 (this equation describe the sequence)

->
`a_n` =
`a_n_-_1` -3;
`a_1` =27

`a_2` =
`a_1` -3 = 27-3 => 24 (this equation doesn't satisfy the sequence)

->
`a_n` =3
`a_n_-_1` -
`(1)/(3)` ;
`a_1` =27

`a_2` =3
`a_1` -
`(1)/(3)` = 3(27)-
`(1)/(3)` => 80.6 (this equation doesn't satisfy the sequence)