Question

Classify each sequence as arithmetic, geometric, or neither by dragging it into the correct box.

Arithmetic Geometric Neither
5/9,5/3,5,15,45,…16,11,6,1,−4,…1/2,1,2,3,4

Answer 1

For the answer to the question above asking to classify each sequence as arithmetic, geometric, or neither by dragging it into the correct box.

These are Geometric
(5/9,5/3,5,15,45)
These ones are Arithmetic
(16,11,6,1,−4)
The last ones are neither which is
(1/2,1,2,3,4)
I hope my answer helped you.

Answer 2

Explanation:

We have been given three sequences:

Case1:

`(5)/(9),\frac{5}[3},5,15,45`

First, we will check ratio of consecutive terms if ratio is same it will be common ratio.

We can check common ratio as:

`\text{common ratio}=(a_2)/(a_1)`

`((5)/(3))/((5)/(9))=3`

`(5)/((5)/(3))=3`

`(15)/(5)=3`

`(45)/(15)=3`

Hence, its a geometric series.

Case2:

16,11,6,1,-4

we will check the difference between consecutive terms

`\text{common difference}=a_2-a_1`

`11-16=-5`

`6-11=-5`

`1-6=-5`

`-4-1=-5`

Hence, this is an arithmetic sequence.

Case3:

`(1)/(2),1,2,3,4`

We will check common ratio as in Case1:

There is no common ratio

We will common difference there is no common difference in the sequence

Hence, this is neither a geometric nor an arithmetic sequence.