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).
How To Solve TRICKY Problem Only 18% Of Mathematicians Could Solve
This puzzle went viral in the discrete mathematics community because so many people got it wrong! You roll a fair dice until you get a 6. What is the expected number of rolls, including the roll of 6, conditioned on the event that all previous rolls (if any) were even numbers? Gil Kalai di
From playlist Statistics And Probability
6 Coin Flips to get 2 Tails in a Row on Average ?!? Here is Why !
Imagine you have a coin. You want to do coin flips until you get two tails in a row. How many coin flips should you expect to do in average to get two tails in a row ? Are you able to solve this problem ? If not, don't worry, that's what I'm doing in this video ! I also find a formula for
From playlist Summer of Math Exposition Youtube Videos
Arithmetico-Geometric Series Visualized (visual proof using Gabriel's Staircase)
This is a short, animated visual proof computing the sum of the differentiated geometric series with terms of the form k times r^k where r is between 0 and 1. The proof uses a fascinating object called Gabriel's staircase, which has infinite perimeter but encloses a finite area. #mathβ #in
From playlist Infinite Series
What is the definition of a geometric sequence
π 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
What is the definition of an arithmetic sequence
π 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
What is an arithmetic sequence
π 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
Determine if a sequence is geometric or not
π 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
Determine if a sequence is geometric or not
π 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
How to determine if a sequence is arithmetic or geometric
π 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
What is arithmetic sequences and how do we determine them
π 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
What are the formulas for arithmetic and geometric sequences
π 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
Elliptic Curves - Lecture 1 - Introduction to diophantine equations
This video is part of a graduate course on elliptic curves that I taught at UConn in Spring 2021. The course is an introduction to the theory of elliptic curves. More information about the course can be found at the course website: https://alozano.clas.uconn.edu/math5020-elliptic-curves/
From playlist An Introduction to the Arithmetic of Elliptic Curves
Define an Arithmetic and Geometric Sequence
This video defines and give two examples of arithmetic and geometric sequences. Site: http://mathispower4u.com Blog: http://mathispower4u.wordpress.com
From playlist Sequences
Geometric Series and Geometric Sequences - Basic Introduction
This algebra and precalculus video tutorial provides a basic introduction into geometric series and geometric sequences. It explains how to calculate the common ratio of a geometric sequence and how to determine the nth term of a geometric sequence. It explains how to write a general equ
From playlist New Calculus Video Playlist
Geometric Sequences (Precalculus - College Algebra 71)
An introduction to Geometric Sequences, how they are created, the form they take, and how to find the general term of a geometric sequence from a list of numbers. Support: https://www.patreon.com/ProfessorLeonard Professor Leonard Merch: https://professor-leonard.myshopify.com
From playlist Precalculus - College Algebra/Trigonometry
2, 4, 8, 16, find the 15th term of the geometric sequence
How to find the nth term of a geometric sequence. For more in-depth math help check out my catalog of courses. Every course includes over 275 videos of easy to follow and understand math instruction, with fully explained practice problems and printable worksheets, review notes and quizze
From playlist Pre-Calculus / Trigonometry
Arithmetic Sequences and Arithmetic Series - Basic Introduction
This video provides a basic introduction into arithmetic sequences and series. It explains how to find the nth term of a sequence as well as how to find the sum of an arithmetic sequence. It also discusses how to distinguish a finite sequence from an infinite series. It also includes a
From playlist New Precalculus Video Playlist
Given a sequence of numbers determine if it is geometric or not
π 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
How to determine if a sequence is geometric or not
π 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