Explanation:
how unusual to call this that way.
I think you (and your teacher) mean the third term in a geometric sequence (or geometric progression, hence GP) between 27 and 1/27 is 1.
that means the sequence goes
27, a2, a3, 1, ..., 1/27
and so, "the number of means" is the number of terms between 27 and 1/27.
I happen to know that 27 is 3³. and that fits perfectly.
a2 = a1/3 = 27/3 = 9
a3 = a2/3 = 9/3 = 3
a4 = q = a3/3 = 3/3 = 1
correct. so, the common ratio is 1/3 (every new term of the sequence is created by multiplying the previous term by 1/3).
and then, if we continue, we get
a5 = a4/3 = 1/3
a6 = a5/3 = 1/3 / 3 = 1/9
a7 = a6/3 = 1/9 / 3 = 1/27
so the terms between 27 and 1/27 are a2, a3, a4, a5 and a6. that are 5 terms "in between" or 5 "means" between 27 and 1/27.