C. Two Consecutive Sums

For an arithmetic series, what would need to be added to \(S_{n - 1} \) to give \(S_n \)? If the last term in the series is \(t_n \), then by adding \(t_n \) to \(S_{n - 1} \), the result is \(S_n \).

\(S_{n - 1} + t_n = S_n \)

Rewritten, you arrive at an important formula.


  Key Lesson Marker


Two Consecutive Sums

\(S_n - S_{n - 1} = t_n \)

Apply this formula in Example 3.