Question

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 ...

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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.

Answer 6

Okay so how should I determine he answer?

Answer 7

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.

Answer 8

Okay.

Answer 9

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

Answer 10

2

Answer 11

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

Answer 12

4

Answer 13

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

Answer 14

Okay.

Answer 15

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

Answer 16

Okay.

Answer 17

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

Answer 18

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

Answer 19

8

Answer 20

The fractions are what gets me.

Answer 21

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

Answer 22

Then do the same for the other 2 choices.

Answer 23

okay.
Thank you!