Arithmetic Progression

Formulas:

• The common difference:
  $d = a_2 - a_1 = a_3 - a_2 = a_4 - a_3 = ~ ...$
• The n^th term:
  $a_n = a_m + (n - m)d$
• Sum of the first n terms of AP:
  $S_n = \frac{1}{2}n(a_1 + a_n) = \frac{1}{2}n \big[ \, 2a_1 + (n - 1)d \, \big]$