Sequence and Series 1 - Arithmetic Progression (AP)

Grade 11 · Mathematics

Semester 1 | Period 2 | Week 9

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Subject: Mathematics

Semester: 1

Period: 2

Week: 9

WEEK 9

Class: Grade 11
Age: 16 years
Duration: 40 minutes of 5 periods
Subject: Mathematics
Topic: Sequence and Series 1 - Arithmetic Progression (AP)
Focus: Meaning of sequences, first term (a), common difference (d), nth term of an A.P., arithmetic mean, sum of an A.P., and practical problem-solving.

SPECIFIC OBJECTIVES:

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

  1. Understand and define sequences, particularly Arithmetic Progression (A.P.).
  2. Identify the first term (a), common difference (d), and nth term of an Arithmetic Progression.
  3. Derive the formula for the nth term of an A.P.
  4. Calculate the nth term of an A.P.
  5. Calculate the arithmetic mean and sum of an A.P.
  6. Solve practical problems involving real-life situations using A.P. concepts.

INSTRUCTIONAL TECHNIQUES:

  • Guided discovery
  • Question and answer
  • Demonstration
  • Discussion
  • Problem-solving activities
  • Real-life examples

INSTRUCTIONAL MATERIALS:

  • Whiteboard and markers
  • Visual aids (e.g., age of students, poles, pillars, objects of different sizes)
  • Charts showing examples of A.P. in real-life contexts
  • Worksheets for practice problems

  1. Find the arithmetic mean of 3 and 7.
  2. Calculate the sum of the first 5 terms of the sequence 6, 10, 14, 18, ...
  3. What is the sum of the first 4 terms of the A.P. 2, 5, 8, 11, 14, ...?
  4. Find the sum of the first 12 terms of the A.P. 2, 4, 6, 8, ...
  5. Calculate the arithmetic mean of 5 and 9.

ASSIGNMENT (5 tasks):

  1. Find the sum of the first 8 terms of the A.P. 4, 8, 12, 16, ...
  2. Calculate the arithmetic mean of 11 and 19.
  3. Find the sum of the first 6 terms of the sequence 10, 15, 20, 25, ...
  4. Calculate the 10th term of the A.P. 3, 6, 9, 12, ...
  5. What is the sum of the first 20 terms of the A.P. 7, 10, 13, 16, ...?

 

PERIOD 5: Practical Problem Solving on A.P.

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Problem Context

Introduces real-life scenarios where A.P. is used, such as in calculating the number of objects in a pattern or salary increments.

Students engage in the problem-solving process, offering their ideas for real-life applications of A.P.

Step 2 - Example Problem

Solves a practical problem: If a person receives a salary increase of 1000 Naira every month, starting from 20,000 Naira, how much will they earn after 6 months?

Students follow the explanation and work through the problem together.

Step 3 - Guided Practice

Provides additional real-life word problems for students to solve using A.P. formulas.

Students solve problems in pairs and ask questions when needed.

Step 4 - Conclusion

Summarizes the lesson, reviewing the key concepts of A.P., arithmetic mean, and sum of an A.P.

Students recap the lesson and clarify any doubts.

EVALUATION (5 exercises):

  1. A person starts with a salary of 10,000 Naira and receives a monthly increase of 500 Naira. What will be their salary after 12 months?
  2. If the first term of an A.P. is 7 and the common difference is 3, what is the sum of the first 5 terms?
  3. A student saves 500 Naira every week, starting with 200 Naira. How much will the student have after 10 weeks?
  4. In a building, the number of floors increases by 2 every year. How many floors will the building have after 5 years if it starts with 10 floors?
  5. Find the sum of the first 6 terms of an A.P. 1, 4, 7, 10, ...

CLASSWORK (5 questions):

  1. Calculate the sum of the first 5 terms of an A.P. 3, 6, 9, 12, 15.
  2. A car travels 50 meters in the first second, 100 meters in the second, 150 meters in the third second, etc. How far will the car have traveled after 6 seconds?
  3. If a person saves 1000 Naira every month starting from 5000 Naira

, how much will they have saved in 9 months? 4. What is the sum of the first 6 terms of the sequence 5, 10, 15, 20, 25, ...? 5. Find the arithmetic mean of 12 and 20.

ASSIGNMENT (5 tasks):

  1. A child saves 200 Naira every week, starting with 100 Naira. How much will they have after 6 weeks?
  2. Calculate the 10th term of the A.P. 2, 5, 8, 11, ...
  3. Find the sum of the first 8 terms of the A.P. 1, 3, 5, 7, ...
  4. A building increases its floors by 3 every year, starting with 15 floors. How many floors will the building have after 7 years?
  5. If the common difference in an A.P. is 6, and the first term is 2, what is the sum of the first 10 terms?