### Mathematics Class XI

Unit-I: Sets and Functions
Chapter 1: Sets
Unit-II: Algebra
Chapter 5: Binomial Theorem
Chapter 6: Sequence and Series
Unit-III: Coordinate Geometry
Chapter 1: Straight Lines
Chapter 2: Conic Sections
Unit-IV: Calculus
Unit-V: Mathematical Reasoning
Unit-VI: Statistics and Probability
Chapter 1: Statistics
Chapter 2: Probability

# Geometric Mean (G.M.)

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:

Note -:

The terms are called the geometric means between and .

(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.

Then,

Then

Where is the base of the logarithm.

This shows that is a GP, with first term and common ratio .

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