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

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.