# Arithmetic mean formula and definition explained

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.