arithmetic series - the expression formed by adding the terms of an arithmetic sequence

Use is the sum of the first n terms. Write a rule for the n^{th} term using the a_{1} and d values. Find the nth term by substituting the value of n into the rule. Substitute the n, a_{1}, and a_{n} values into to find the sum.

Substitute the sum for S_{n}. Substitute the first term for a_{1}. Substitute the rule for a_{n}. Solve for n. If you get a quadratic equation, solve by factoring or the quadratic formula. Choose the positive value.