### 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

# Arithmetic Mean (A.M.)

When three numbers and are in A.P., then is average of and .

Then

In general if are in A.P, their Arithmetic Mean A.M is defined as

Note -:

The terms are called the Arithmetic Means between and .

(i) If a fixed number is added to (subtracted from) each term of a given AP, then the resulting sequence is also an AP and it has the same common difference as that of the given AP.

(ii) If each term of an AP is multiplied by a fixed constant (or divided by a non-zero fixed constant), then the resulting sequence is also an AP.

(iii) If and are two Arithmetic Progressions, then is also an AP.

(iv) If we have to take three terms in AP whose sum is known, it is convenient to take them as . In general, if we take terms in AP, we take them as .

(v) The numbers are said to be Arithmetic Means between and , if is an AP.

Here is the first term and is the term of the AP.

If is the common difference of this AP, then

Thus,

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