This is in Algebra 1 and I would like to know if I am doing this right.

9. Is the following sequence an Arithmetic Sequence? If yes, what is the common difference?

128, 64, 32, 16, ...

I said "Yes It is an Arithmetic Sequence and the common difference is - 1/2

10. Is the following sequence an Arithmetic Sequence? If yes, what is the common difference?

3, 3.25, 3.5, 3.75, ...

I said "Yes it is an Arithmetic Sequence and the common difference is +.25

9) It is not arithmetic. (It is actually geometric.)

10) It is arithmetic. The common difference is 0.25.

Step-by-step explanation:

Arithmetic sequences have common difference where as geometric sequences have a common ratio.

Common difference-you are getting the same difference every time you do term minus previous term.

Common ratio-you are getting the same quotient every time you do term divided by previous term.

So anyways let's look at your first question.

9) Is 128, 64, 32,16, ... arithmetic?

Let's test it!

64-128=-64

32-64=-32

16-32=-16

This is not arithmetic because this is not the same difference every time we do term minus previous term.

However, the sequence is geometric since we get the same quotient when doing term divided by previous term.

That is,

64/128=0.5

32/64=0.5

16/32=0.5

So this sequence is geometric and has common ratio 0.5.

The sequence is not arithmetic as we determined from doing term minus previous and not getting the same difference each time.

10.) Is 3,3.25,3.5,3.75, ... arithmetic?

Let's test it!

3.25-3=0.25

3.5-3.25=0.25

3.75-3.5=0.25

This is arithmetic because we are getting the same difference each time. This is called a common difference that we are getting and that number is 0.25.