anonymous
  • 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 ...
Mathematics
chestercat
  • chestercat
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mathstudent55
  • mathstudent55
Do you know the difference between an arithmetic sequence and a geometric sequence?
anonymous
  • anonymous
No, I haven't learned about geometric sequence yet.
mathstudent55
  • 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
  • anonymous
arithmetic sequence is A sequence made by adding the same value each time.
mathstudent55
  • 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
  • anonymous
Okay so how should I determine he answer?
mathstudent55
  • 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
  • anonymous
Okay.
mathstudent55
  • mathstudent55
Subtract the first term from the second term: what is 4 - 2 = ?
anonymous
  • anonymous
2
mathstudent55
  • mathstudent55
Good. Now subtract the second term form the third term. What is 8 - 4 = ?
anonymous
  • anonymous
4
mathstudent55
  • mathstudent55
Good. The two differences are different. You don't have a common difference, therefore the first choice is NOT an arithmetic sequence.
anonymous
  • anonymous
Okay.
mathstudent55
  • mathstudent55
Remember, in an arithmetic, the difference between any term and the previous term is always the same.
anonymous
  • anonymous
Okay.
anonymous
  • anonymous
Thank you for your help!... I needed that.
mathstudent55
  • mathstudent55
Now try choice B. Do the same thing. What is 4 - 12 = ?
anonymous
  • anonymous
8
anonymous
  • anonymous
The fractions are what gets me.
mathstudent55
  • mathstudent55
Good. Then do 4/3 - 4 = ? If these two differences are not equal, it is not an arithmetic sequence.
mathstudent55
  • mathstudent55
Then do the same for the other 2 choices.
anonymous
  • anonymous
okay. Thank you!

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