# High School Math : Finding Partial Sums in a Series

## Example Questions

### Example Question #1 : Finding Partial Sums In A Series

Find the sum of all even integers from  to .

Explanation:

The formula for the sum of an arithmetic series is

,

where  is the number of terms in the series,  is the first term, and  is the last term.

We know that there are  terms in the series. The first term is  and the last term is . Our formula becomes:

### Example Question #2 : Finding Partial Sums In A Series

Find the sum of all even integers from  to .

Explanation:

The formula for the sum of an arithmetic series is

,

where  is the number of terms in the series,  is the first term, and  is the last term.

### Example Question #3 : Finding Partial Sums In A Series

Find the sum of the even integers from  to .

Explanation:

The sum of even integers represents an arithmetic series.

The formula for the partial sum of an arithmetic series is

,

where  is the first value in the series,  is the number of terms, and  is the difference between sequential terms.

Plugging in our values, we get: