Lesson Notes By Weeks and Term v5 - Grade 11
Number patterns – Week 6 focus
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Number patterns – Week 6 focus
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Subject: Mathematics
Class: Grade 11
Term: 1st Term
Week: 6
Theme: General lesson support
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Number patterns are a fundamental part of mathematics, appearing in various forms and applications. In this week's focus, we will delve deeper into quadratic sequences and series. Understanding these patterns helps us predict future values, model real-world phenomena, and develop critical thinking skills. In a South African context, analyzing trends in population growth, financial investments, or even sports statistics relies heavily on understanding patterns. Imagine being able to predict the future electricity demand based on past consumption patterns, or understanding the growth of a micro-enterprise loan using a quadratic sequence.
Quadratic Sequences: A quadratic sequence is a sequence in which the second difference between consecutive terms is constant. This is different from arithmetic sequences where the first difference is constant. To identify a quadratic sequence, calculate the first differences (the difference between consecutive terms) and then calculate the second differences (the difference between consecutive first differences). If the second difference is constant, the sequence is quadratic. The general term of a quadratic sequence is given by: T n = an 2 + bn + c where a, b, and c are constants, and n represents the term number (n ∈ N). Finding the General Term (T n = an 2 + bn + c): The constants a, b, and c can be found using the following relationships based on the first three terms of the sequence (T 1 , T 2 , T 3 ) and their differences: 2a = Second Difference 3a + b = First Difference between T 1 and T 2 a + b + c = T 1