SOLUTION: Insert 3 geometric means between 16 and 81

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Question 1093779: Insert 3 geometric means between 16 and 81
Answer by ikleyn(52790) About Me  (Show Source):
You can put this solution on YOUR website!
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They want you construct the 5-term geometric progression starting 16 and ending 81:

16 = a,  ar,  ar^2,  ar^3,  ar^4 = 81.


Hence,  r^4 = %28ar%5E4%29%2Fa = 81%2F16.


Thus  r = root%284%2C+81%2F16%29 = +/- 3%2F2 is the common ratio of the progression.


So, you have two ways to construct the required progression:


1)  16,  16%2A%283%2F2%29 = 24,  24%2A%283%2F2%29 = 36,  36%2A%283%2F2%29 = 54,  54%2A%283%2F2%29 = 81,    and


2)  16, -24, 36, -54, 81.

Solved.


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On geometric progressions,  see the introductory lessons
    - Geometric progressions
    - The proofs of the formulas for geometric progressions
    - Problems on geometric progressions
    - Word problems on geometric progressions
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic
"Geometric progressions".