Lesson Notes By Weeks and Term v4 - SHS 2
APPLICATION OF ALGEBRA
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APPLICATION OF ALGEBRA
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Subject: Additional Mathematics
Class: SHS 2
Term: 1st Term
Week: 5
Grade code: 2.1.1.LI.3
Strand code: 1
Sub-strand code: 1
Content standard code: 2.1.1.CS.2
Indicator code: 2.1.1.LI.3
Theme: MODELLING WITH ALGEBRA
Subtheme: APPLICATION OF ALGEBRA
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This lesson explores two important types of "averages" or "means" that arise from sequences: the Arithmetic Mean (AM) and the Geometric Mean (GM). We already know about arithmetic and geometric progressions (APs and GPs), which model patterns of growth we see all around us in Ghana. For instance, a driver adding a fixed amount of money to his daily sales is following an AP, while the value of an investment growing by a certain percentage each year follows a GP. Today, we will learn how to find the 'middle values' or means in these sequences.
A. Recap: Arithmetic and Geometric Progressions
Before we discuss their means, let's refresh our memory on the two types of sequences. Arithmetic Progression (AP): A sequence where each term is found by adding a constant value, the common difference (d), to the previous term. Example: 3, 7, 11, 15, ... (Here, `d = 4`) Formula for the nth term: `U_n = a + (n-1)d` Geometric Progression (GP): A sequence where each term is found by multiplying the previous term by a constant value, the common ratio (r). Example: 2, 6, 18, 54, ... (Here, `r = 3`) Formula for the nth term: `U_n = ar^(n-1)`
*(Teacher's Note: Use a quick 'Talk for Learning' activity. Ask students in pairs to create one example of an AP and one of a GP and share with the class.)* B. The Arithmetic Mean (AM)
The arithmetic mean is the average you are most familiar with. In the context of an AP, it's the term(s) that lie in between two other terms.