Question

Find the three geometric means between 2 and 162.

Answer 1

a = 2

a5 = 162

ar^4 = 162

Answer 2

r^4 = 81

r = 3

Answer 3

2 , 6 , 18 , 54 , 162

Answer 4

Let's make three blanks between them:
2 _ _ _ 162
First, find the geometric mean of \(2\) and \(162\). Say it is \(n\).
2 _ \(n\) _ 162
Then find the geometric mean of \(2\),\(n\) and \(n,162\).

Answer 5

Good trick, but realize that \(r\) could also be \(-3\). :D