Middle Term of an AP

Middle Term of an AP

## Conditions / Special Cases

If the number of terms is odd:

$$n=2m+1$$

then the middle term is:

$$a_{m+1}$$

and:

$$a_{m+1}=\frac{a_1+a_n}{2}$$

If the number of terms is even:

$$n=2m$$

the two middle terms are:

$$a_m,\ a_{m+1}$$

and their average is:

$$\frac{a_m+a_{m+1}}2=\frac{a_1+a_n}{2}$$

## Usage

- Used to find middle terms and exploit symmetry in APs.