Question

Use the geometric mean to find the 7th term in a geometric sequence if the 6th term is 50 and the 8th term is 18.

Answer 1

A geometric sequence means you're multiplying by the same number over and over again to get each term in the sequence. Let's call that number x. So to get from the 6th to the 7th, you multiply the 6th by x, and to get from the 7th to the 8th, you multiply by x again.

This information is enough to set up an equation to solve for x. Can you give it a shot?

Answer 2

I just dont get how I'm supposed to start if I don't know what x is

Answer 3

You can set up an equation. You take 50 and multiply it by x, and then multiply it by x again, and now you're at 18. What would that look like as an equation, and how can you solve for x?

Answer 4

50x^2=18?

Answer 5

would I divide 50 by 18?

Answer 6

no, 18 by 50

Answer 7

Right?

Answer 8

Yes. If you simplify the fraction, this will be a much easier problem.

Answer 9

I got .36 after dividing 18 by 50.

Answer 10

simplified it's 9/25

Answer 11

Okay, so don't forget about the x^2...you're not done solving for x quite yet.

Answer 12

I'm so confused. I don't know where to put anything

Answer 13

Here's what you've done so far.

50x^2 = 18

x^2 = 18/50

x^2 = 9/25

Now how do you get rid of the "^2"?

Answer 14

take the square root?

Answer 15

Yes. And when you take the square root of a fraction, you just square root the top and square root the bottom. So what do you get for x?

Answer 16

3/5?

Answer 17

Yes! So now you have the number that you need to multiply by each time to get every term in the sequence: 3/5.

So if the 6th term is 50, what is the 7th term?

Answer 18

30. Thank you so much!

Answer 19

Good job. You're welcome.