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An arithmetic-geometric progression (AGP) is a progression in which each term can be represented as the product of the terms of an arithmetic progressions (AP) and geometric progressions (GP).
An arithmetic progression (AP) is a sequence of numbers such that the difference between the consecutive terms is constant. How do we find the sum of the first 10 terms? It is not convenient to add all the individual terms to obtain the sum. There is a formula to find the sum of the first 'n' terms of an AP. Natural numbers, whole numbers and integers are examples of arithmetic progressions.
An arithmetic progression is a list of numbers in which each term is obtained by adding a fixed number to the preceding term, except the first term.
This fixed number is called the common difference of the AP. It can be positive, negative or zero>
Eg: 1, 2, 3, 4, . . . is an arithmetic progression.
Each of the numbers in the list is called a term.
The common difference in this case is equal to 1 = 2 – 1= 3 – 2 = 4 – 3 = ….
An arithmetic progression having a finite number of terms is called a finite arithmetic progression.
An arithmetic progression having an infinite number of terms is called an infinite arithmetic progression.
In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-one number called the common ratio. For example, sequence 2, 6, 18, 54, … is a geometric progression with common ratio 3.
A Geometric progression is a list of numbers in which each term is obtained by multiplying or dividing a fixed number to the preceding term, except the first term.
This fixed number is called the common ratio of the GP.
E.g., 2, 4, 8, 16, . . . is a geometric progression as each term of it multiplied by 2 gives its next term. (Clearly, common ratio r = 2).