Common Difference

Common Difference

## Formula

For an AP:

$$d=a_2-a_1=a_3-a_2=\cdots=a_n-a_{n-1}$$

Also:

$$d=\frac{a_n-a}{n-1}$$

## Conditions / Special Cases

If:

$$d>0$$

the AP is increasing.

If:

$$d<0$$

the AP is decreasing.

If:

$$d=0$$

all terms are equal.

## Usage

- Used to identify an AP and determine its common difference.