How do you find the geometric means in each sequence 1/24, __, __, __, 54124,_,_,_,54?
1 Answer
Jan 1, 2017
The three geometric means are:
1/414 ,3/232 and99
Explanation:
The general term of a geometric sequence can be written as:
a_n = a*r^(n-1)an=a⋅rn−1
where
If
r^4 = (a r^4)/(a r^0) = a_5/a_1 = 54/(1/24) = 54*24 = 1296 = 6^4r4=ar4ar0=a5a1=54124=54⋅24=1296=64
This has two Real solutions and two non-Real Complex solutions:
r = +-6" "r=±6 or" "r = +-6i 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), 54124,14,32,9,54
