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Lesson Plan Maths Class X (Ch-5) | Arithmetic Progression
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TEACHER'S NAME : DINESH KUMAR | SCHOOL : RMB DAV CENTENARY PUBLIC SCHOOL NAWANSHAHR |
SUBJECT : MATHEMATICS | CLASS : X STANDARD BOARD : CBSE |
LESSON TOPIC / TITLE : CHAPTER 13: Arithmetic Progression | ESTIMATED DURATION: This topic is divided into seven modules and are completed in fifteen class meetings. |
- Knowledge of sequence and series.
- Motivation for studying Arithmetic Progression (AP).
- Derivation of nth term of an AP.
- Derivation of the formula to find the nth term from the end of the sequence.
- Derivation of sum to n terms of an AP.
- Application of the formulas of AP to solve the daily life problems.
- Sequence, Series and Arithmetic Progression.
- All formulas and all important concepts related to the Arithmetic progression.
- Students should be able to find the nth term of the AP from the starting and from the end of the sequences.
- Students should also be able to find the sum to n terms of the AP from the starting and from the end of the sequences.
Introduction :
Start the session by explaining the terms sequence and series.
Sequence
If different terms are separated by commas then it is called sequence
Example : 2, 5, 7, 9, 11, 12, …..
Series :
If different terms are separated by “+” or “-“ then it is called series.
Example : 2 + 5 + 7 + 9 + 11 + 12 + ….
Arithmetic Progression:
Now teacher will introduce the concept of Arithmetic Progression(AP), to the students. Teacher may write few sequences on the board and explain the difference between the A.P. and the other sequences.
General or n^{th} Term of an AP
Now teacher will write general A.P. on the board and explain its term and common difference.
a, a + d, a + 2d, a + 3d, …….. a + (n - 1)d
With the help of these terms find the formula for general term of an A.P.
a_{n} or t_{n} = a + (n - 1)d
Where :
a is the first term,
n is the number of terms
d is the common difference.
Teacher will also help the students in the implementation of this formula in different problems.
General Term from the end of the AP sequence
Now teacher will explain the method of finding the general terms of an AP from the end of the sequence. The formula derived is given below
a_{n} or t_{n} = l - (n-1)d
Where:
l is the last term of the sequence
n is the number of terms
d is the common difference
Students should be given sufficient number of problems for practice and implementation of the formula.
Sum to n terms of an AP
Now teacher will introduce the formula for finding sum to n terms of an AP and explain its components and the derivation.
Where :
a is the first term
n is the number of terms
d is the common difference
l is the last term
Teacher will assign sufficient number of problems to the students for practice.
Sum to n terms from the end of an AP
Now teacher will introduce the formula for finding sum to n terms from the end of an AP and explain its components and the derivation.
Where: l is the last term of the sequence.
Teacher will assign some problems based on the implementation of this formula.
Taking 3, 4, 5 terms in AP
Teacher will also provide the knowledge to the students, of taking three, four and five terms in an AP.
Three terms in an AP can be taken as
a - d, a, a + d
Four terms in an AP can be taken as
a - 3d, a - d, a + d, a + 3d
Five terms in an AP can be taken as
a - 2d, a - d, a, a + d, a + 2d
Applications:
Now teacher will assign some word problems based on our daily life situations and help the students in the implementations of the above formulas in these problems.
- Review questions given by the teacher.
- Students should prepare the presentation on the derivation of the formula for finding the nth term of the sequence and the formula for finding the sum to n terms from the starting and end of the sequence.
- Solve N.C.E.R.T. problems with examples.
- Solve assignment on Multiple Choice Questions (MCQ) given by the teacher.
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