# Lesson Plan: Arithmetic Progression (A.P.)
## Subject: Mathematics
## Grade Level: Senior Secondary 2
## Duration: 1 Hour
### Objective:
By the end of this lesson, students should be able to:
1. Define and identify an arithmetic progression.
2. Derive and use the nth-term formula of an arithmetic sequence.
3. Calculate the sum of the first n terms of an arithmetic progression.
### Materials:
- Whiteboard and markers
- Graphing calculator
- Projector and computer (optional)
- Printed handouts with practice problems
- Notebook and pencils for students
### Introduction (10 minutes):
1. Begin with a brief review of sequences (mentioning geometric and arithmetic sequences).
2. Introduce the concept of Arithmetic Progression (A.P.):
- Definition: An arithmetic progression is a sequence of numbers in which the difference between consecutive terms is constant.
- Example: 2, 4, 6, 8, … (here, the common difference, d, is 2).
### Teaching Activities (30 minutes):
#### A. Explanation and Derivation (15 minutes):
1. **Nth Term of A.P.**:
- General form: `a, a+d, a+2d, a+3d, …`
- Derive the nth term formula:
\[ a_n = a + (n-1)d \]
where \( a \) is the first term, \( d \) is the common difference, and \( n \) is the term position.
2. **Example 1**:
- Find the 10th term of the series: 3, 7, 11, 15, ….
- Solution:
\[ a = 3, d = 4, n = 10 \]
\[ a_{10} = 3 + (10-1)4 = 3 + 36 = 39 \]
#### B. Sum of the First n Terms of A.P. (15 minutes):
1. **Sum Formula**:
- Derive the formula for the sum of the first \( n \) terms:
\[ S_n = \frac{n}{2} [2a + (n-1)d] \]
2. **Example 2**:
- Calculate the sum of the first 20 terms of the series: 5, 8, 11, 14, …
- Solution:
\[ a = 5, d = 3, n = 20 \]
\[ S_{20} = \frac{20}{2} [2 \times 5 + (20-1) \times 3] \]
\[ S_{20} = 10 [10 + 57] \]
\[ S_{20} = 10 \times 67 = 670 \]
### Guided Practice (10 minutes):
- Distribute handouts with practice problems.
- Work through at least one problem together as a class:
- Problem: Find the 15th term and the sum of the first 15 terms of the series: 7, 10, 13, …
- Solution:
\[ a = 7, d = 3 \]
- \(15th\) term:
\[ a_{15} = 7 + (15-1)3 = 7 + 42 = 49 \]
- Sum of the first 15 terms:
\[ S_{15} = \frac{15}{2} [2 \times 7 + (15-1) \times 3] \]
\[ S_{15} = \frac{15}{2} [14 + 42] \]
\[ S_{15} = \frac{15}{2} \times 56 \]
\[ S_{15} = 15 \times 28 = 420 \]
### Independent Practice (5-10 minutes):
- Students individually work on additional practice problems from the handout.
- Examples:
1. Find the 12th term and the sum of the first 12 terms of the series: 1, 4, 7, 10, …
2. Calculate the 8th term and the sum of the first 8 terms of the series: 2, 5, 8, 11, …
### Conclusion (5-10 minutes):
1. Review key concepts.
2. Allow students to ask questions.
3. Assign homework consisting of additional problems on arithmetic progression for further practice.
### Assessment:
- Monitor students' progress during guided and independent practice.
- Evaluate the completion and accuracy of the practice problems.
- Homework will be reviewed in subsequent classes to ensure understanding.
### Homework:
- Complete problems involving finding the nth term and the sum of n terms for given arithmetic sequences from the textbook.
### Reflection:
- Assess the overall understanding of the students regarding the concept of arithmetic progression.
- Note areas where students showed difficulty and plan to revisit those specific areas in the next class or provide further practice.
By following this structured plan, you will ensure that students gain a solid understanding of arithmetic progressions, essential for their subsequent math courses and subjects involving sequences and series.