In mathematics, a series is a sequence of numbers where the difference between successive numbers is constant. This constant is often referred to as the "common difference" and is denoted by d . The first term of the series is represented by a1 , and the total number of terms in the series is represented by n.

The sum of an arithmetic series can be calculated by multiplying the number of terms by the average of the first and last term. This is a key concept in understanding the series formula.

The formula to calculate the sum of the terms of an arithmetic series is as follows:

Working through an Example

Example: Consider an arithmetic series 5 + 9 + 13 + 17 + ··· + 101. Here, the first term a1 = 5 and the common difference d = 4. We are to find the total number of terms n , using the formula for an arithmetic series.

Solution:

To find n , we solve the equation 5 + ( n – 1) x 4 = 101. Solving this gives n = 25.