Mathematical series | Articles containing proofs | Sequences and series

Geometric progression

In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio. For example, the sequence 2, 6, 18, 54, ... is a geometric progression with common ratio 3. Similarly 10, 5, 2.5, 1.25, ... is a geometric sequence with common ratio 1/2. Examples of a geometric sequence are powers rk of a fixed non-zero number r, such as 2k and 3k. The general form of a geometric sequence is where r ≠ 0 is the common ratio and a ≠ 0 is a scale factor, equal to the sequence's start value. The distinction between a progression and a series is that a progression is a sequence, whereas a series is a sum. (Wikipedia).

Geometric progression
Video thumbnail

Intro to Geometric Progressions (1 of 3: Definitions)

More resources available at www.misterwootube.com

From playlist Modelling Financial Situations

Video thumbnail

What is the definition of a geometric sequence

👉 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

Video thumbnail

Series & Sequences Introduction (3 of 3: Geometric Progressions)

More resources available at www.misterwootube.com

From playlist Modelling Financial Situations

Video thumbnail

How to determine the rule for a geometric sequence given two values

👉 Learn how to write the explicit formula for a geometric sequence. 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. A geometric sequence is a sequence in which each term of the sequence is obtained by multi

From playlist Sequences

Video thumbnail

Intro to Geometric Progressions

More resources available at www.misterwootube.com

From playlist Modelling Financial Situations

Video thumbnail

Geometric Series

This video introduces geometric series. http://mathispower4u.yolasite.com/

From playlist Series (Algebra)

Video thumbnail

Learn how to determine the sum of a geometric finite series

👉 Learn how to find the geometric sum of a series. A series is the sum of the terms of a sequence. A geometric series is the sum of the terms of a geometric sequence. The formula for the sum of n terms of a geometric sequence is given by Sn = a[(r^n - 1)/(r - 1)], where a is the first term

From playlist Series

Video thumbnail

How to find the first five terms of a geometric sequence

👉 Learn how to find the first 5 terms of a geometric sequence. 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. A geometric sequence is a sequence in which each term of the sequence is obtained by multiplyin

From playlist Sequences

Video thumbnail

Arithmetic Progression and Geometric Progression | Don't Memorise | (GMAT/GRE/CAT/Bank PO/SSC CGL)

Arithmetic Progression (AP) and Geometric Progression (GP) - Both super important concepts explained in this video. To learn more about Arithmetic Progression, enroll in our full course now: https://infinitylearn.com/microcourses?utm_source=youtube&utm_medium=Soical&utm_campaign=DM&utm_c

From playlist Arithmetic Progression Class 10

Video thumbnail

IMS Public Lecture: Butterflies, Cats, and Billiards in Polygons

Anton Zorich, Université Paris Diderot - Paris 7, France

From playlist Public Lectures

Video thumbnail

Sum of a finite GP (geomtric progression)

Support me on Patreon: https://www.patreon.com/mathsaurus This video explains how to add together the terms of a geometric sequence, demonstrating and explaining the formula used. Visit http://www.mathsaurus.com/ for more free GCSE and A-level maths videos and resources Visit the Mat

From playlist C1 C2 Sequences APs and GPs

Video thumbnail

The sum of a series is the limit of its partial sums -- Calculus II

This lecture is on Calculus II. It follows Part II of the book Calculus Illustrated by Peter Saveliev. The text of the book can be found at http://calculus123.com.

From playlist Calculus II

Video thumbnail

Discrete Math II - 8.2.1 Solving First-Order Linear Homogeneous Recurrence Relations

We take another look at First-Order Linear Homogeneous Recurrence relations (and what exactly all of that means). We took our first look in section 8.1 by using back substitution and iteration. In this video we look at one example using both methods, then dive into further detail on how to

From playlist Discrete Math II/Combinatorics (entire course)

Video thumbnail

Sum to infinity of a GP (geometric progression)

Explains how to find the sum of an infinite geometric sequence, including how to use the formula as well as when and why it is valid. ______________________________________ Free online maths challenge courses: Primary (age 9-11): https://bit.ly/primarymathschallenge Junior (age 10-13):

From playlist C1 C2 Sequences APs and GPs

Video thumbnail

Write the first five terms of the geometric sequence

👉 Learn how to find the first 5 terms of a geometric sequence. 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. A geometric sequence is a sequence in which each term of the sequence is obtained by multiplyin

From playlist Sequences

Video thumbnail

Arithmetic Progression And Geometric Progression With Examples (AP & GP) | Simplilearn

This video covers the fundamentals of arithmetic progression and geometric progression. It explains how to calculate the nth term of a sequence and the sum of the n terms. There are also a few numerical problems. 🔥Free Data Science Course with Completion Certificate: https://www.simplilea

From playlist 🔥Data Science | Data Science Full Course | Data Science For Beginners | Data Science Projects | Updated Data Science Playlist 2023 | Simplilearn

Related pages

Exponential decay | Exponentiation | Absolute value | If and only if | Extended real number line | Summation | Derivative | Logarithm | Geometric mean | Absolute convergence | Number | Arithmetic progression | Geometric series | Point at infinity | Power of two | Sequence | Banach algebra | Euler's formula | Stirling numbers of the second kind | Euclid's Elements | Mathematics | Exponential growth | Euclid | Constant function | Arithmetic mean | Series (mathematics) | Scale factor | 1/2 + 1/4 + 1/8 + 1/16 + ⋯ | Complex number | 1/2 − 1/4 + 1/8 − 1/16 + ⋯ | Alternating series | Linear function (calculus)