Arithmetic Mean of Terms of an AP

Arithmetic Mean of Terms of an AP

## Formula

For an AP:

$$a,a+d,a+2d,\ldots,a+(n-1)d$$

the arithmetic mean of all $$n$$ terms is:

$$\frac{a+l}{2}$$

where $$l$$ is the last term.

Also:

$$\text{Mean}=\frac{S_n}{n}$$

Therefore:

$$\frac{S_n}{n}=\frac{a+l}{2}$$

## Usage

- Used to calculate the average of all terms of an AP quickly.