Question

Arithmetic, Geometric, or Neither Classify each sequence as arithmetic, geometric, or neither. (matching) 4/9, 4/3, 4, 12, 36. 0, 1, 2, 3, 4, 5, 6. -10, -6, -2, 2, 6, 10.

Answer 1

The given sequence is neither arithmetic not geometric.

Explanation:

A sequence is in arithmetic if it has a common difference.

i.e., a sequence a, b, c is in arithmetic if

b - a = c - b

Let's check if the given sequence is in arithmetic.

`(4)/(3) -(4)/(9) =(12)/(9) -(4)/(9)`

`= (8)/(9)`

`4-(4)/(3) =(12-4)/(3)`

`=(8)/(3)`

So,
`(4)/(3) -(4)/(9) \\eq 4-(4)/(3)`

Hence, the given sequence is not arithmetic.

Let's check if the given sequence is in geometric.

A sequence is in geometric if it has a common ratio.

i.e., a sequence a, b, c is in geometric if

`(b)/(a) =(c)/(b)`

`(4/3)/(4/9) =(4)/(3) ((9)/(4) )`

= 3

`(4)/(4/3) =4((3)/(4) )`

= 3

Clearly,
`(12)/(4) =(36)/(12) =3`

But,
`(0)/(36) =0`

Therefore, the given sequence is not in geometric.

Hence, the given sequence is neither arithmetic not geometric.