Properties of an AP

Properties of an AP

## Formula

If:

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

is an AP, then:

$$a_r-a_s=(r-s)d$$

Also:

$$a_{r+k}-a_r=kd$$

For equally spaced indices:

$$a_{r-k}+a_{r+k}=2a_r$$

## Conditions / Special Cases

Three consecutive terms of an AP satisfy:

$$2b=a+c$$

if the terms are:

$$a,b,c$$

## Usage

- Used to establish relations between terms without calculating the entire sequence.