OpenStudy (anonymous):

SOMEONE PLEASE HELP ME!!!!! I need to find the next three numbers on this sequence! I can't do this one

OpenStudy (anonymous):

OpenStudy (mathstudent55):

Sequences are often either arithmetic or geometric. Are you familiar with those terms?

OpenStudy (anonymous):

Yes.

OpenStudy (mathstudent55):

In an arithmetic sequence, the same number (called the common difference) is added to each number of the sequence to produce the next number.

OpenStudy (mathstudent55):

Can you check if this is an arithmetic sequence?

OpenStudy (anonymous):

This is Geometric. Right?

OpenStudy (mathstudent55):

Yes, this is a geometric sequence. In a geometric sequence, each number is multiplied by the same number (called the common ratio) to produce the next number. Can you find the common ratio of this sequence?

OpenStudy (anonymous):

I don't know how. I am stuck on this one and my brain won't work for me.

OpenStudy (mathstudent55):

It's easier than you think. Since when you multiply a number by the common ratio you get the next number, if you divide a number by the previous number, you get the common ratio.

OpenStudy (anonymous):

Is it 4?

OpenStudy (mathstudent55):

No. Divide a number by the previous number, not by the next number.

OpenStudy (mathstudent55):

What is 4 divided by 16? What is 1 divided by 4? What is 1/4 divided by 1? etc. Since this is a geometric sequence, all those divisions will give you the same answer, the common ratio.

OpenStudy (anonymous):

4 divided by 16 = .25 =1/4

OpenStudy (mathstudent55):

Correct. All those divisions will give you the same answer, 1/4. That means 1/4 is the common ratio. Now when you multiply a number in the sequence by 1/4, you get the next number.

OpenStudy (anonymous):

oh okay.

OpenStudy (mathstudent55):

The last number you have given in the sequence is 1/16. What is the next number?

OpenStudy (anonymous):

1/64

OpenStudy (mathstudent55):

Good. What's the next one?

OpenStudy (anonymous):

1/256

OpenStudy (mathstudent55):

Right. What about the next one?

OpenStudy (anonymous):

1/1024

OpenStudy (anonymous):

Thank you so much!

OpenStudy (mathstudent55):

Exactly. See, you did it yourself! You're welcome.