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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

Verified Answer :

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:

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

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

We can check common ratio as:

\(\text{common ratio}=\frac{a_2}{a_1}\)

\(\frac{\frac{5}{3}}{\frac{5}{9}}=3\)

\(\frac{5}{\frac{5}{3}}=3\)

\(\frac{15}{5}=3\)

\(\frac{45}{15}=3\)

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:

\(\frac{1}{2},1,2,3,4\)

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.

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