# How do you find the geometric means in each sequence #1/24, __, __, __, 54#?

##### 1 Answer

Jan 1, 2017

The three geometric means are:

#1/4# ,#3/2# and#9#

#### Explanation:

The general term of a geometric sequence can be written as:

#a_n = a*r^(n-1)#

where

If

#r^4 = (a r^4)/(a r^0) = a_5/a_1 = 54/(1/24) = 54*24 = 1296 = 6^4#

This has two Real solutions and two non-Real Complex solutions:

#r = +-6" "# or#" "r = +-6i#

Since the question asks about geometric means and the given terms are positive, we can probably assume that we want the positive common ratio

Hence the sequence is:

#1/24, color(blue)(1/4), color(blue)(3/2), color(blue)(9), 54#