Arithmetic Progression (AP) An arithmetic progression (AP) is a sequence of numbers such that the difference between any two consecutive numbers is constant...
Arithmetic Progression (AP)
An arithmetic progression (AP) is a sequence of numbers such that the difference between any two consecutive numbers is constant. This constant difference is called the common difference or the arithmetic difference.
The general term of an AP with the first term a and common difference d is given by the formula:
where n is the position of the term in the sequence.
Geometric Progression (GP)
A geometric progression (GP) is a sequence of numbers such that the ratio between any two consecutive numbers is constant. This constant ratio is called the common ratio or the geometric ratio.
The general term of a GP with the first term a and common ratio r is given by the formula:
where n is the position of the term in the sequence.
Key Differences
The main difference between AP and GP is that the difference between consecutive numbers in AP is constant, while the ratio between consecutive numbers in GP is constant. Additionally, the terms in AP are arranged in order of increasing values of n, while the terms in GP are arranged in order of decreasing values of n.
Examples
AP
GP