An arithmetic sequence (or arithmetic progression, AP) is an ordered set of numbers in which the difference between consecutive values is constant. For example:
2, 6, 10, 14, 18, 22, …
The sum of a sequence is called a series. For example:
2 + 6 + 10 + 14 + 18 + 22 + …
The general term in an arithmetic sequence is given by
[pmath size=11]a_k = a + (k – 1)d[/pmath]
The sum of the first [pmath size=11]n[/pmath] terms of an arithmetic sequence is given by
[pmath size=11]S_n = n / 2 (2a + (n-1)d)[/pmath]
where
- a = first term
- ak = kth term
- d = common difference
- k = term number
- n = number of terms
- Sn = sum of first n terms of sequence
