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

1. Use  is the sum of the first n terms.
2. Write a rule for the n^th term using the a₁ and d values.
3. Find the nth term by substituting the value of n into the rule.
4. Substitute the n, a₁, and a_n values into  to find the sum.

1. Substitute the sum for S_n.
2. Substitute the first term for a₁.
3. Substitute the rule for a_n.
4. Solve for n.
• If you get a quadratic equation, solve by factoring or the quadratic formula.
• Choose the positive value.