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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

Respuesta :

MissPhiladelphia
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:

Step-by-step explanation:

We have been given three sequences:

Case1:

[tex]\frac{5}{9},\frac{5}[3},5,15,45[/tex]

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

We can check common ratio as:

[tex]\text{common ratio}=\frac{a_2}{a_1}[/tex]

[tex]\frac{\frac{5}{3}}{\frac{5}{9}}=3[/tex]

[tex]\frac{5}{\frac{5}{3}}=3[/tex]

[tex]\frac{15}{5}=3[/tex]

[tex]\frac{45}{15}=3[/tex]

Hence, its a geometric series.

Case2:

16,11,6,1,-4

we will check the difference between consecutive terms

[tex]\text{common difference}=a_2-a_1[/tex]

[tex]11-16=-5[/tex]

[tex]6-11=-5[/tex]

[tex]1-6=-5[/tex]

[tex]-4-1=-5[/tex]

Hence, this is an arithmetic sequence.

Case3:

[tex]\frac{1}{2},1,2,3,4[/tex]

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.

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