Average of Terms in an Arithmetic Progression

Average of Terms in an Arithmetic Progression

## Formula

If the terms of an AP are:

$$a_1,a_2,\ldots,a_n$$

then:

$$\text{Average}=\frac{a_1+a_2+\cdots+a_n}{n}$$

Since:

$$S_n=\frac n2(a_1+a_n)$$

we get:

$$\text{Average}=\frac{a_1+a_n}{2}$$

## Usage

- Used in average-related problems involving equally spaced values.