The document defines arithmetic series as a sequence of numbers where each term is found by adding a constant amount (called the common difference) to the previous term. It provides the general formula for an nth term in an arithmetic series as Tn = a + (n-1)d, where a is the first term and d is the common difference. As an example, it calculates the general term for a series where T3 = 9 and T7 = 21, finding the common difference is 3 and the first term is also 3, giving the general term as Tn = 3n - 3.