Arithmetic Progression

A sequence of numbers is called an Arithmetic progression if the difference between any two consecutive terms is always the same. In simple terms, it means that the next number in the series is calculated by adding a fixed number to the previous number in the series. For example, 2, 4, 6, 8, 10 is an AP because difference between any two consecutive terms in the series (common difference) is same (4 – 2 = 6 – 4 = 8 – 6 = 10 – 8 = 2).

Fact about Arithmetic Progression :

1. Initial term: In an arithmetic progression, the first number in the series is called the initial term.
2. Common difference: The value by which consecutive terms increase or decrease is called the common difference.
3. The behavior of the arithmetic progression depends on the common difference d. If the common difference is:positive, then the members (terms) will grow towards positive infinity or negative, then the members (terms) will grow towards negative infinity.

Formula of nth term of an A.P :
If ‘a’ is the initial term and ‘d’ is the common difference.Thus, the explicit formula is

Formula of sum of nth term of A.P: