Arithmetic progression

An arithmetic progression (AP) is a sequence of numbers where the difference between any two consecutive terms is always the same. This difference is called the common difference, usually denoted by $d$. The $n$th term of an AP with first term $a$ is given by $a_n = a + (n-1)d$.

Important properties

• The difference between any two consecutive terms is constant.

• The $n$th term formula: $a_n = a + (n-1)d$.

• The sum of the first $n$ terms: $S_n = \frac{n}{2}(2a + (n-1)d)$.