Sum of Terms in an AP with General Starting Index

Sum of Terms in an AP with General Starting Index

## Formula

For:

$$\sum_{k=m}^{n}[a+(k-1)d]$$

the number of terms is:

$$n-m+1$$

Therefore:

$$\sum_{k=m}^{n}[a+(k-1)d]=\frac{n-m+1}{2}[2a+(m+n-2)d]$$

## Usage

- Used to calculate partial sums of an AP when the summation does not start from the first term.