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- anonymous

Which of the following is an arithmetic sequence?
2, 4, 8, 16, ...
12, 4, 4/3, 16/3 ...
1/2, -1/2, -3/2, -5/2 ...
1/2, -1/2, 1/2, -1/2 ...

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- anonymous

- chestercat

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- mathstudent55

Do you know the difference between an arithmetic sequence and a geometric sequence?

- anonymous

No, I haven't learned about geometric sequence yet.

- mathstudent55

In an arithmetic sequence each term minus the previous term is always the same difference. That is called the common difference.

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- anonymous

arithmetic sequence is A sequence made by adding the same value each time.

- mathstudent55

Ok. Then we will only discuss the arithmetic sequence.
Start with the second term, and subtract the first term from it. You get a difference.
Then subtract the second term from the third term. Subtract the third term from the fourth term. If the difference is always the same, that is the common difference and it is an arithmetic sequence.

- anonymous

Okay so how should I determine he answer?

- mathstudent55

Let's start with the first choice.
You need to do this to all the choices, but we'll use the first choice to do together.

- anonymous

Okay.

- mathstudent55

Subtract the first term from the second term:
what is 4 - 2 = ?

- anonymous

2

- mathstudent55

Good.
Now subtract the second term form the third term.
What is 8 - 4 = ?

- anonymous

4

- mathstudent55

Good.
The two differences are different. You don't have a common difference, therefore the first choice is NOT an arithmetic sequence.

- anonymous

Okay.

- mathstudent55

Remember, in an arithmetic, the difference between any term and the previous term is always the same.

- anonymous

Okay.

- anonymous

Thank you for your help!... I needed that.

- mathstudent55

Now try choice B.
Do the same thing.
What is 4 - 12 = ?

- anonymous

8

- anonymous

The fractions are what gets me.

- mathstudent55

Good.
Then do 4/3 - 4 = ?
If these two differences are not equal, it is not an arithmetic sequence.

- mathstudent55

Then do the same for the other 2 choices.

- anonymous

okay.
Thank you!

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