GENERATING PATTERN | ARITHMETIC SEQUENCE FORMULA (English)
86This is a Module based lesson for MATH 10 with the topic GENERATING PATTERN as well as SOLVING PROBLEMS USING ARITHMETIC SEQUENCE FORMULA for Quarter 1 Weeks 1 - 2.
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Lesson Goals and Targets
solve and generate patterns
Illustrate an arithmetic sequence
solve for the nth term, find the general rule for solving an arithmetic sequence and solve for the common difference given only 2 nth terms.
Lesson Flow:
0:00 Sneak Peak Preview
1:40 Introduction
2:10 Lesson Goals and Targets
2:31 What are patterns or sequences?
2:44 Application of patterns in real life
3:17 example of number sequences
4:17 counting numbers
4:55 skip counting
5:18 connection of 2 sequences
8:18 Concept of common difference
8:58 Example #1 Easy
9:48 Example #2 Easy
12:09 Arithmetic Sequence Formula
13:59 Example #3 Easy
16:10 Example #4 Easy
19:00 Example #5 Average
25:11 Example #6 Challenge
30:44 Closing message and references
You may also watch connected videos:
intro to geometric sequence/geometric vs arithmetic: https://youtu.be/7MVdw9CxdCM
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video Highlights:
Many professions that use mathematics are interested in one specific aspect – finding patterns, and being able to predict the future. Here are a few examples:
In the last decade, police departments around the world have started to rely more on mathematics. Special algorithms can use the data of past crimes to predict when and where crimes might occur in the future.
It turns out that earthquakes follow similar patterns to crimes. Just like one crime might trigger retaliations, an earthquake might trigger aftershocks. In mathematics, this is called a “self-exciting process”, and there are equations that help predict when the next one might happen.
In mathematics, a sequence is a chain of numbers (or other objects) that usually follow a pattern. It can be either infinite or finite. The individual elements in a sequence are called terms. The terms of a sequence are all its individual numbers or elements.
Here are some examples:
When you began school as a young child, you were immediately introduced to a simple number sequence. You learned to recite all the counting numbers. Usually by the end of Kindergarten, most children can count from 1 to 100. The rule is simply: "Add 1." By applying this rule repeatedly, an unending list of numbers can be created.
Compare the 2nd term from the 1st list with the 2nd term from the 2nd list. Compare each pair of corresponding terms. Can you tell what the relationship is between the lists? Do you understand why? Each corresponding term on the second list is five times as big as the term on the first list. Why do you think that is?
The key is in the two rules that were used to generate the sequences. Since the rule "Add 10" is adding five times as much as the rule "Add 2," The terms on the second list are five times as big as the terms on the first list.
The sequences that we have shown are called arithmetic sequence. An arithmetic sequence is a list of numbers with a definite pattern. If you take any number in the sequence then subtract it by the previous one, and the result is always the same or constant. Look at this pattern that we have. The constant difference in all pairs of consecutive or successive numbers in a sequence is called the common difference, denoted by the letter d. We use the common difference to go from one term to another.
If the common difference between consecutive terms is positive, we say that the sequence is increasing.
On the other hand, when the difference is negative, we say that the sequence is decreasing.
an = the term that you want to find
a1 = first term in the list of ordered numbers
n = the term position (ex: for 5th term, n = 5 )
dd = common difference of any pair of consecutive or adjacent numbers
Let’s put this formula in action!
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#MELCMath10 #Mathematics10 #firstquarterunit1 #mathfirstquarter #patternandsequence #arithmeticsequence #arithmeticpattern #solvingfornthterm #solvingforcommondifference #generatepatterns #nthterm #generalrule #Whatarepatternsorsequences? #Applicationofpatternsinreallife #countingnumbers #skipcounting #commondifference #ArithmeticSequenceFormula #tutorials #predictthefuture #crimes #algorithms #module