Arithmetic Mean
Definition:
In sequences and series, the arithmetic mean refers to the average of two numbers in a sequence, especially in an arithmetic progression (AP).
Arithmetic Mean between Two Terms in an AP:
For an arithmetic progression with terms $a$ and $b$, the arithmetic mean of $a$and $b$ is calculated as:
$\text{ArithmeticMean}=\frac{a+b}{2}$
Where:
 $a$ and $b$ are consecutive terms in the AP.
 The arithmetic mean is the term exactly in the middle of $a$ and $b$.
Properties and Usage:

Midpoint in an AP:
 The arithmetic mean represents the midpoint between two terms in an AP.

Formula within an AP:
 Helps in finding an intermediate term between two given terms.
Example:
Consider an AP with terms $5$and $15$.
To find the arithmetic mean:
$\text{ArithmeticMean}=\frac{5+15}{2}=\frac{20}{2}=10$
So, the arithmetic mean between $5$ and $15$ in this AP is $10$.
Relationship to Arithmetic Progression:
 In an arithmetic progression, the arithmetic mean between any two consecutive terms is constant.
 The arithmetic mean can also be viewed as the term that divides any two consecutive terms into equal parts.