Mathematical series

Arithmetico-geometric sequence

In mathematics, arithmetico-geometric sequence is the result of term-by-term multiplication of a geometric progression with the corresponding terms of an arithmetic progression. Put plainly, the nth term of an arithmetico-geometric sequence is the product of the nth term of an arithmetic sequenceand the nth term of a geometric one. Arithmetico-geometric sequences arise in various applications, such as the computation of expected values in probability theory. For instance, the sequence is an arithmetico-geometric sequence. The arithmetic component appears in the numerator (in blue), and the geometric one in the denominator (in green). The summation of this infinite sequence is known as an arithmetico-geometric series, and its most basic form has been called Gabriel's staircase: The denomination may also be applied to different objects presenting characteristics of both arithmetic and geometric sequences; for instance the French notion of arithmetico-geometric sequence refers to sequences of the form , which generalise both arithmetic and geometric sequences. Such sequences are a special case of linear difference equations. (Wikipedia).

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From playlist Statistics And Probability

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From playlist Summer of Math Exposition Youtube Videos

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From playlist Infinite Series

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From playlist Sequences

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What is the definition of an arithmetic sequence

πŸ‘‰ Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which

From playlist Sequences

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From playlist Sequences

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From playlist Sequences

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Determine if a sequence is geometric or not

πŸ‘‰ Learn how to determine if a sequence is arithmetic, geometric, or neither. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric seque

From playlist Sequences

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πŸ‘‰ Learn how to determine if a sequence is arithmetic, geometric, or neither. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric seque

From playlist Sequences

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From playlist Sequences

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From playlist Sequences

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From playlist An Introduction to the Arithmetic of Elliptic Curves

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From playlist Sequences

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From playlist New Calculus Video Playlist

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From playlist Precalculus - College Algebra/Trigonometry

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From playlist Pre-Calculus / Trigonometry

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From playlist New Precalculus Video Playlist

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πŸ‘‰ Learn how to determine if a sequence is arithmetic, geometric, or neither. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric seque

From playlist Sequences

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How to determine if a sequence is geometric or not

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From playlist Sequences

Related pages

Coin flipping | Series (mathematics) | Geometric progression | Arithmetic progression | Divergent series | Geometric series | Mathematics | Probability theory | Closed-form expression | Alternating series | Telescoping series