HOW DO WE GET THE FORMULA OF ARITHMETIC MEAN?

The students have already known about the formula of arithmetic mean that they have known and used for years. To find the mean of two numbers, add then and then divide the sum by two.
But, Can you find out the way to get that formula?
Actually, it is a simple way to get the formula of arithmetic mean. But sometime, people do not really know about it.

Everyone has known about the arithmetic formula:

We then use the concept just presented to find the missing middle term, or arithmetic mean, if the first and third terms of an arithmetic sequence are given. To begin I use an example.
If we are given that a, n, b are three consecutive terms in an arithmetic sequence, how do we find the value of n?

If we call the common different "d " the the following statements can be made:

Then, if we add the both sides:

Thus, we get the formula of arithmetic mean:

Source: Robin S. Kalder, Ed.D. Jurnal International "Geometric Mean - What does it mean?".

^_^ Selamat Belajar ^_^