Question

Find the three geometric means between 1/2 and 8.
im not really sure how to do this.

Answer 1

Think of it like this:
You need to insert one number in each blank so that the resulting sequence is geometric:
\[\frac{1}{2},\ \_\_\_ ,\ \_\_\_,\ \_\_\_, 8 \]

Answer 2

umm okay. but how would I find the numbers that go in between?

Answer 3

I'll outline it step by step:
1. Divide the last number by the first number. Call this k.
2. Take this root: \(\sqrt[n]{k}\) where n is the number of blanks+1. Call this r.
3. Multiply the first number by r, then multiply this by r, etc. until all the blanks are filled. To check whether r is correct, make sure you get the last number correctly.

Answer 4

okay thanks I understand now :)