Lesson Notes By Weeks and Term v4 - SHS 1

Lesson Video

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Performance objectives

• Identify linear and exponential sequences.
• Find the nth term of these sequences.
• Solve real-life problems using sequences.

Lesson summary

This lesson introduces learners to sequences, which are ordered lists of numbers that follow a specific rule or pattern. We see patterns everywhere in Ghana – in the designs of our Kente and Smock fabrics, in the way houses are arranged in a new estate, and even in how a farmer might increase their planting of yam seedlings each year. By understanding the algebra behind these patterns, we can predict future values, plan for growth, and solve complex real-world problems related to finance, population, and more. We will focus on two main types of sequences: linear (arithmetic) and exponential (geometric).

Lesson notes

A. What is a Sequence? A sequence is a list of numbers, called terms, arranged in a definite order. Each term is related to the previous one by a specific rule. Example: 2, 4, 6, 8, ... (The rule is "add 2 to the previous term"). Example: 3, 9, 27, 81, ... (The rule is "multiply the previous term by 3").

We use notation like `U_n` to represent the term in the nth position. `U_1` is the first term. `U_2` is the second term. `U_n` is the general or nth term. B. Linear Sequences (Arithmetic Progressions - A.P.) A linear sequence is one where the difference between consecutive terms is constant. This constant difference is called the common difference (d). Key Features: First Term (a): The starting number of the sequence. Common Difference (d): The fixed amount you add to get from one term to the next. You can find it by subtracting any term from the term that follows it (`d = U_2 - U_1`). Deriving the Formula for the nth term: First term: `U_1 = a` Second term: `U_2 = a + d` Third term: `U_3 = (a + d) + d = a + 2d` Fourth term: `U_4 = (a + 2d) + d = a + 3d` Observing the pattern, the nth term will be: `U_n = a + (n-1)d`

Evaluation guide

• Find the nth term of linear and exponential sequences.
• Collaborative Learning: Learners will work in convenient groups (ability, mixed -ability, mixed
• gender etc.) to solve problems and present answers.
• Talk for Learning Approaches: Learners will be engaged through think -pair-share in