Lesson Notes By Weeks and Term v4 - SHS 2

Lesson Video

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Performance objectives

• Define and differentiate recursive and explicit formulas.
• Generate terms of a sequence using recursive formulas.
• Convert between recursive and explicit forms.
• Apply sequences to model real-life situations.
• Analyze geometric series, especially for recurring decimals.

Lesson summary

This lesson introduces learners to the powerful idea of using sequences to model real-world situations. We often see patterns around us, from the way our mobile money balance grows with interest to the spread of information in a community. Algebra, specifically through sequences, gives us the tools to describe these patterns mathematically, predict future outcomes, and make informed decisions. By understanding recursive and explicit formulae, we can create precise models for these dynamic situations. This skill is not just for examinations; it is a foundational concept in finance, science, and technology.

Lesson notes

A. What is a Sequence?

A sequence is simply an ordered list of numbers. Each number in the list is called a term. We often use the notation `T_n` to represent the *n*-th term. For example, in the sequence `5, 8, 11, 14, ...` The first term, `T_1 = 5` The second term, `T_2 = 8` The *n*-th term, `T_n`, represents the term in the *n*-th position.

There are two primary ways to define the rule for a sequence: explicitly and recursively. B. Explicit Formula

An explicit formula defines the *n*-th term of a sequence as a function of its position, *n*. It allows you to find any term directly without needing to know the previous terms. Think of it as a direct calculation machine: You put in the position number `n`, and it gives you the term `T_n`.

Evaluation guide

• Use recursive and explicit formulae of sequences to model situations and translate between
• the two forms.
• Collaborative Learning: Talk for Learning Approaches, Project -based Learning
• Experiential Learning and Problem -based Learning