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#
