Arithmetic mean (A.M.)

If $x$ and $y$ are two numbers, their Arithmetic Mean is $A=\dfrac{x+y}2$. This is precisely the value that makes $x, A, y$ an A.P., since $A-x=y-A \Rightarrow 2A=x+y \Rightarrow A=\dfrac{x+y}2$.

For example, the Arithmetic Mean of 4 and 10 is $A=\dfrac{4+10}2=7$, and indeed 4, 7, 10 is an A.P. This single-mean case is the simplest instance of a more general idea covered later in the chapter: inserting n arithm …