SOLUTION: given a and b, suppose that three numbers are inserted between them so that the five numbers form a geometric sequence. if the product of the three numbers between a and b is 27, s

Question 1143590: given a and b, suppose that three numbers are inserted between them so that the five numbers form a geometric sequence. if the product of the three numbers between a and b is 27, show that ab is equal to 9.
Answer by ikleyn(52790) (Show Source): You can put this solution on YOUR website!
.

Then "the product of the tree numbers between a and b" is the cube of the very middle term, which, hence, is equal to  = 3.


Further, the three numbers  "a", 3  and "b"  form a geometric progression.


For every geometric progression, the middle of any three consecutive terms is the geometric mean of the two extreme terms.


So,  then   = 3,  which implies  ab = 9.

Q.E.D.

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There is a bunch of lessons on geometric progressions in this site
    - Geometric progressions
    - The proofs of the formulas for geometric progressions
    - Problems on geometric progressions
    - Solved problems on geometric progressions
    - Word problems on geometric progressions
    - One characteristic property of geometric progressions (*)
    - Fresh, sweet and crispy problem on arithmetic and geometric progressions

Especially, see the lesson (*) from the list.

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".

Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.

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