SOLUTION: 160, __, __, __, __, 5 Insert four geometric means between 160 and 5. What is the first of these geometric means?

Algebra ->  Sequences-and-series -> SOLUTION: 160, __, __, __, __, 5 Insert four geometric means between 160 and 5. What is the first of these geometric means?      Log On


   

Question 964933: 160, __, __, __, __, 5
Insert four geometric means between 160 and 5. What is the first of these geometric means?
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Let the common ratio be r.  Then the sequence is:

160, 160r=%22%3F%22, 160r%5E2=%22%3F%22, 160r%5E3=%22%3F%22, 160r%5E4=%22%3F%22, 160r%5E5=5

We solve the equation

160r%5E5=5
r%5E5=5%2F160
r%5E5=1%2F32
r=root%285%2C1%2F32%29
r=1%2F2

Therefore the sequence is

160, 80, 40, 20, 10, 5

The first of these four inserted means between 160 and 5 is 80.

Edwin