Arithmetic Sequences

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

a_k = a + (k - 1)d

The sum of the first n terms of an arithmetic sequence is given by

S_n = n / 2 (2a + (n-1)d)

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