# 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 = (p+r)/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 (3+17)/2 = 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 = (6+k)/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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