Lesson Notes By Weeks and Term v4 - SHS 2
PATTERNS AND RELATIONS
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PATTERNS AND RELATIONS
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Subject: Mathematics
Class: SHS 2
Term: 1st Term
Week: 16
Grade code: 2.2.2.LI.3
Strand code: 2
Sub-strand code: 2
Content standard code: 2.2.2.CS.1
Indicator code: 2.2.2.LI.3
Theme: ALGEBRAIC REASONING
Subtheme: PATTERNS AND RELATIONS
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This lesson introduces learners to Geometric Progressions (GPs), a special type of sequence where numbers grow or shrink by a constant multiplicative factor. This pattern is seen all around us in Ghana. Think about how a popular video spreads on social media, how money grows with compound interest in a bank, or even how certain populations grow. Understanding GPs helps us model this kind of "exponential" change, which is a powerful tool in finance, science, and technology. This lesson builds on our previous work with Arithmetic Progressions but shifts from adding a constant difference to multiplying by a constant ratio.
A. What is a Geometric Progression?
A Geometric Progression (GP), also known as an exponential 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. First Term (a): The starting number of the sequence. Common Ratio (r): The constant factor you multiply by. To find the common ratio, you can divide any term by its preceding term. `r = (Second Term) / (First Term) = U₂ / U₁` `r = (Third Term) / (Second Term) = U₃ / U₂`
Teacher-Led Example 1: Identifying `a` and `r`
Consider the sequence: 5, 15, 45, 135, ... Is this a GP? Let's check the ratio between terms. `15 / 5 = 3` `45 / 15 = 3` `135 / 45 = 3` Since the ratio is constant, it is a GP. What is the first term (a)? The first number in the sequence is 5. So, `a = 5`. What is the common ratio (r)? The constant multiplier we found is 3. So, `r = 3`.