Arithmetic series

The idea

An arithmetic sequence adds the same difference $d$ each time. The $n$th term is $a + (n - 1)d$ and the sum of the first $n$ terms is $S_n = \frac{n}{2}[2a + (n - 1)d]$.

1. Find $a$ (first term) and $d$ (common difference).
2. For a term: $u_n = a + (n - 1)d$.
3. For a sum: $S_n = \frac{n}{2}[2a + (n - 1)d]$, or $\frac{n}{2}(a + l)$ with last term $l$.

Watch out $n$ terms have $n - 1$ gaps: the $n$th term is $a + (n - 1)d$.