GEOMETRIC SEQUENCE | GEOMETRIC VS. ARITHMETIC SEQUENCE: English
38This is a Module based lesson for MATH 10 with the topic of introduction to GEOMETRIC SEQUENCE and comparing GEOMETRIC with ARITHMETIC SEQUENCE in a lot of aspects for Quarter 1 Week 3.
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Lesson goals and targets
Define and illustrate geometric Sequence.
Application of geometric sequence in real life.
Differentiate geometric sequence from arithmetic sequence.
Lesson Flow:
0:00 Sneak Peek Preview
1:49 Introduction
2:49 Lesson Goals and Targets
3:20 Difference of Sequence and Progression
3:49 What is Geometric sequence?
4:21 How to create a geometric sequence?
6:12 Notations of geometric sequence
8:22 How to test a sequence if it is geometric?
10:49 two versions of geometric formula
12:13 applications of geometric sequence
14:43 geometric sequence vs arithmetic sequence
14:54 In terms of: Definition
15:44 in terms of Calculations
16:04 in terms of Formula
16:44 in terms of Form
17:04 in terms of application
18:04 Closing message and references
You may also watch connected videos:
generating sequence or patterns/arithmetic sequence: https://youtu.be/VbAWMHIBuYI
Video Highlighted Script:
The terms “sequence” and “progression” are interchangeable.
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-zero number called the common ratio.
Pick a number, any number, and write it down. For example: 2.
Now pick a second number, any number (I’ll choose 3), which we will call the common ratio. Now multiply the first number by the common ratio, then write their product down to the right of the first number: 6. Now, continue multiplying each product by the common ratio (3 in my example) and writing the result down… over, and over, and over:. By following this process, you have created a “Geometric Sequence”, a sequence of numbers in which the ratio of every two successive terms is the same.
2 is the first term (also called the starting term) of the sequence. To refer to the first term of a sequence, mathematicians use the notation a sub 1. This notation is read as “A sub one”. The one is a “subscript” (value written slightly below the line of text) and indicates the position of the term within the sequence.
all the terms in a Geometric Sequence must be the same multiple this factor is given a formal name (the common ratio). If you multiply any term by this value, you end up with the value of the next term.
The common ratio can be positive or negative. It can be a whole number, a fraction, or even an irrational number. No matter what value it has, it will be the ratio of any two consecutive terms in the Geometric Sequence.
Therefore, to test if a sequence of numbers is a Geometric Sequence, calculate the ratio of successive terms in various locations within the sequence. If by the end of our solution, we have calculated the same ratio between any two adjacent terms chosen from the sequence. Then it is a Geometric Sequence.
HOW TO: GIVEN A SET OF NUMBERS, DETERMINE IF THEY REPRESENT A GEOMETRIC SEQUENCE.
Divide each term by the previous term.
Compare the quotients. If they are the same, a common ratio exists, and the sequence is geometric.
References:
https://mathmaine.com/2014/05/08/summary-geometric-sequences-and-series/
https://courses.lumenlearning.com/boundless-algebra/chapter/geometric-sequences-and-series/
http://home.windstream.net/okrebs/page131.html
https://askanydifference.com/difference-between-arithmetic-and-geometric-sequence/
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