If three terms numbers and form a G.P, then is said to be the Geometric Mean (G.M) of and .
Here (common ratio)
is always positive.
Therefore geometric mean between and is or .
Geometric Mean of terms in G.P
If are n positive numbers in G.P, then their Geometric Mean is defined as:
The terms are called the geometric means between and .
Some Facts about G.P -:
(i) If each term of a GP is multiplied (divided) by a fixed non-zero constant, then the resulting sequence is also a GP.
(ii) If are two geometric progressions, then the sequence is also in GP.
(iii) If we have to take three terms in GP, then we take them as and four terms as .
(iv) If is a GP then is an AP.
Suppose is a GP.
Let , where , is the first term and is the common ratio of the GP.
Where is the base of the logarithm.
This shows that is a GP, with first term and common ratio .