SOLUTION: Geometric mean of 2 4 8 16 32 64

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Question 1185706: Geometric mean of 2 4 8 16 32 64
Found 3 solutions by math_helper, greenestamps, ikleyn:
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!


+root%286%2C+2%2A4%2A8%2A16%2A32%2A64%29+=+11.314+ (rounded to three decimal places)

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The sequence itself is geometric; so the geometric mean is simply the geometric mean of the first and last terms:

sqrt%282%2A64%29+=+8%2Asqrt%282%29

ANSWER: 8*sqrt(2)

Answer by ikleyn(52790) About Me  (Show Source):
You can put this solution on YOUR website!
.

Geometric mean of n terms  a%5B1%5D, a%5B2%5D, . . . , a%5Bn%5D is,  BY THE DEFINITION,  the root of degree n  of the product of these terms


    GM%28a%5B1%5D%2C+a%5B2%5D%2C+ellipsis%2C+a%5Bn%5D%29 = root%28n%2C+a%5B1%5D%2Aa%5B2%5D%2Aellipsis%2Aa%5Bn%5D%29.


In this case, GM(2,4,8,16,32,64) = root%286%2C2%2A4%2A8%2A16%2A32%2A64%29 = root%286%2C2%5E21%29 = 2%5E3%2Asqrt%282%29 = 8%2Asqrt%282%29 = 11.314  (rounded).    ANSWER

Solved.

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On Geometric mean see this Wikipedia article

https://en.wikipedia.org/wiki/Geometric_mean