Further Mathematics - Senior Secondary 1 - Sequences and series (I)

Sequences and series (I)

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TERM: 2ND TERM

WEEK 1
Class: Senior Secondary School 1
Age: 15 years
Duration: 40 minutes of 4 periods
Subject: Further Mathematics
Topic: Sequences and Series (I)
Focus: Definition of Sequences and Series, nth Term of a Sequence, Arithmetic Progression (AP)

SPECIFIC OBJECTIVES:

By the end of the lesson, students should be able to:

  1. Define a sequence and a series.
  2. Identify the difference between a sequence and a series.
  3. Determine the nth term of a given sequence.
  4. Identify and solve problems involving Arithmetic Progression (AP).

INSTRUCTIONAL TECHNIQUES:

  • Guided discussion
    • Question and answer
    • Group work
    • Use of examples and analogies
    • Practice exercises

INSTRUCTIONAL MATERIALS:

  • Charts of common sequences and series
    • Flashcards with arithmetic patterns
    • Whiteboard and markers
    • Worksheets for sequence patterns and nth term

PERIOD 1 & 2: Definition of Sequences and Series, nth Term of a Sequence

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 – Introduction

Introduces the topic by asking students to list numbers that follow a particular pattern (e.g., 2, 4, 6, 8...). Defines sequence as a set of numbers in a particular order.

Students respond by suggesting number patterns and listen attentively.

Step 2 – Explanation

Defines series as the sum of the terms of a sequence. Differentiates clearly between a sequence and a series.

Students take notes and provide more examples.

Step 3 – nth Term

Introduces the formula for the nth term (Tₙ) = a + (n - 1)d where a is the first term, d is the common difference. Works through examples with the class.

Students follow along, solve examples with guidance.

Step 4 – Analogy

Uses analogy of staircases or repeated actions to help students grasp the concept of repeated patterns.

Students relate the concept to daily life examples.

 

NOTE ON BOARD:

  • A sequence is an ordered list of numbers.
  • A series is the sum of the terms in a sequence.
  • Tₙ = a + (n - 1)d (nth term of an AP).
  • Example: Find the 5th term of the sequence: 3, 6, 9...
    T₅ = 3 + (5 - 1) × 3 = 15

 

EVALUATION (5 Exercises):

  1. Define a sequence.
  2. Define a series.
  3. What is the difference between a sequence and a series?
  4. What is the nth term of 5, 10, 15...?
  5. Find the 7th term of the sequence: 2, 5, 8...

 

CLASSWORK (5 Questions):

  1. Identify the 4th term of the sequence: 7, 11, 15...
  2. What is the nth term of 1, 4, 7...?
  3. Find the 6th term of the AP with a = 2 and d = 5.
  4. What is the 10th term of the sequence: 3, 6, 9...?
  5. Is the list 1, 3, 6, 10... a sequence or a series?

 

ASSIGNMENT (5 Tasks):

  1. Write out the first five terms of the sequence whose nth term is Tₙ = 4n + 1.
  2. Explain in your own words the difference between sequence and series.
  3. Identify the 8th term of the sequence: 10, 15, 20...
  4. Create a real-life example of a number sequence.
  5. Research and write one example of a non-arithmetic sequence.

 

PERIOD 3 & 4: Arithmetic Progression (AP)

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 – Introduction

Defines Arithmetic Progression (AP) as a sequence where the difference between any two consecutive terms is constant.

Students listen and provide examples of AP.

Step 2 – General Formula

Introduces the nth term formula for AP: Tₙ = a + (n - 1)d. Explains with different examples.

Students note and solve examples with help.

Step 3 – Finding Terms

Gives problems requiring students to find terms in APs. E.g., find the 12th term of 4, 9, 14...

Students work in pairs or individually to solve.

Step 4 – Guided Practice

Organizes students in small groups to solve various AP problems on the board.

Students participate in group work and present solutions.

 

NOTE ON BOARD:

  • Arithmetic Progression (AP): Tₙ = a + (n - 1)d
  • Example: Find the 12th term of 4, 9, 14...
    a = 4, d = 5
    T₁₂ = 4 + (12 - 1) × 5 = 4 + 55 = 59

EVALUATION (5 Exercises):

  1. Define Arithmetic Progression (AP).
  2. Find the 9th term of the AP: 3, 7, 11...
  3. If a = 5, d = 3, find the 15th term.
  4. What is the formula for the nth term of an AP?
  5. Find the 5th term of the AP: 20, 15, 10...

 

CLASSWORK (5 Questions):

  1. Find the 20th term of the AP: 1, 4, 7...
  2. What is the common difference in the AP: 6, 11, 16...?
  3. Write the first five terms of the AP with a = 2 and d = 6.
  4. Find the 10th term of the AP: 100, 90, 80...
  5. If Tₙ = 2n + 3, find the 6th term.

 

ASSIGNMENT (5 Tasks):

  1. Find the 30th term of the AP: 3, 5, 7...
  2. Create your own AP and write the first ten terms.
  3. Research and write the formula for the sum of the first n terms of an AP.
  4. Find the 25th term of an AP with a = 6 and d = 4.

What is the common difference in the AP: 50, 45, 40...?