Learn and know the **formula for the arithmetic mean** in Arithmetic progression and also know the definition of the arithmetic mean. In shortcut we call **arithmetic mean as A.M**. we can also say **arithmetic mean** as the average of three terms. We all know how to find the average i.e. the sum of all the terms divided with the no. of terms gives us the average.

**Arithmetic mean formula** is considered as one of the important formulae in arithmetic progression concept. So every student should learn what is the **arithmetic mean**? And also know how to find it. Like other formulas in mathematics, it is not that much difficult to remember. Below I have given both definition and formula and also some examples for arithmetic mean, just go through it.

**The definition of the arithmetic mean (A.M):**

Suppose if the terms *p,q,r* are in arithmetic progression then we call the middle term “*q*” as the **arithmetic mean** (A.M). For example, w know that 2, 8, 14 are in ** arithmetic progression**. In the three numbers, the middle term i.e. “8” is called as the arithmetic mean (A.M).

**The Formula for finding Arithmetic Mean:**

If *p, q, r* are in arithmetic progression then “*q*” is called **arithmetic mean (A.M)**. A.M is find out by the formula, *q* = \frac { \left( p+r \right) }{ 2 } .

Note:

If all the three terms are equal i.e. a, a, a are in A.P. then the arithmetic mean is “a” only. Let us consider an example, if 6, 6, 6 are in A.P. then arithmetic mean is “6” only.

Example 1:

If 3, t, 17 are in **arithmetic progression** then find “t”.

Solution:

As we know “t” is **arithmetic mean** and it is given by \frac { \left( 3+17 \right) }{ 2 } = \frac { 20 }{ 2 } = 10. The value of “t” is 10.

Example 2:

Given that 6, 10, *k* are in arithmetic progression then the value of “*k*” is?

Solution:

We know that,

10 = \frac { \left( 6+k \right) }{ 2 }

20 = 6+*k*

20-6 = *k*

14 =*k*

Note:

Without applying **arithmetic mean** we can find the value of “b”. As the three terms are in A.P with common difference 4 so after 10 the next number will be 14.

Hope you have understood what is the meaning of the word A.M. i.e. **arithmetic mean and the formula** for finding the value of it.

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