Question

Determine whether each of the following sequences are arithmetic, geometric or neither. If arithmetic, state the common difference. If geometric, state the common ratio. 4, 13/3, 14/3, 5, 16/3, …​

Answer 1

sequence is arithmetic

Explanation:

An arithmetic sequence has a common difference between consecutive terms.

A geometric sequence has a common ratio between consecutive terms.

given

4 ,
`(13)/(3)` ,
`(14)/(3)` , 5 , that is

`(12)/(3)` ,
`(13)/(3)` ,
`(14)/(3)` ,
`(15)/(3)` , then

`(13)/(3)` -
`(12)/(3)` =
`(14)/(3)` -
`(13)/(3)` =
`(15)/(3)` -
`(14)/(3)` =
`(1)/(3)`

there is a common difference d =
`(1)/(3)` between consecutive terms

thus the sequence is arithmetic