Question

Which describes the difference between the two sequences? First Sequence: 6, 8, 10, 12, ... Second Sequence: 16, 20, 24, 28, ... The first sequence is arithmetic because there is a common difference of 2. The second sequence is geometric because there is a common ratio of 4. Both sequences are geometric. The first sequence has a common difference of 2, and the second sequence has a common difference of 4. The first sequence is geometric because there is a common ratio of 2. The second sequence is arithmetic because there is a common difference of 4. Both sequences are arithmetic. The first sequence has a common difference of 2, and the second sequence has a common difference of 4.

Answer 1

Both sequences are arithmetic. The first sequence has a common difference of 2, and the second sequence has a common difference of 4.

Explanation:

Let's remember the definitions of arithmetic and geometric sequences:

`\fbox {Arithmetic sequence:}` the difference between one term and the next is a constant (always the same), i.e. we add the same value to one term to get the next one.

`\fbox {Geometric sequence:}` each term is found by multiplying the previous term by a constant.

So, in one case we add the same constant and in the other we multiply it.

Let's analyze our sequences:

6, 8, 10, 12, ...

The difference between the first term and the second one is 8 - 6 = 2

The difference between the second term and the third one is 10 - 8 = 2

And the last difference is 12 - 10 = 2

We are adding 2 in each term, so it's an arithmetic sequence.

Let's see it's not a geometric sequence:

We need to multiply 6 by 4/3 to get 8, but if we multiply 8 by 4/3, we get 32/3 and that's not the third term. So, we are not multiplying by a constant in this case.

16, 20, 24, 28, ...

If we do as before, we get that we add 4 in each term to get the next one, so it's an arithmetic sequence.

It's not a geometric sequence because we need to multiply 16 by 5/4 to get 20, but 20 * 5/4 = 25
`\\eq` 24

Answer 2

Both sequences are arithmetic since they have common difference for each of the sequence