Lesson Plan, Class XI Ch-8 | Sequence and Series

LESSON PLAN   SUBJECT MATHEMATICS    CLASS 10+1

lesson plan for maths class XI cbse, lesson plans for mathematics teachers, lesson plan for maths teacher in B.Ed. Lesson Plan, Class XI  For Mathematics Teacher

Rmb dav centnary public school Nawanshahr
NAME OF THE TEACHER				DINESH KUMAR
CLASS	10+1	CHAPTER	08	SUBJECT	MATHEMATICS
TOPIC	SEQUENCE & SERIES			DURATION : 25 CLASS MEETINGS

PRE- REQUISITE KNOWLEDGE:

• Knowledge of number system.

• Knowledge of arithmetic progression class 10^th .

TEACHING AIDS:

Green Board, Chalk,  Duster, Charts, smart board, projector, laptop etc.

METHODOLOGY:

Lecture method, Demonstration and Learning by doing

LEARNING  OBJECTIVES:

• Sequence and Series

• Arithmetic Progressions, their nth term their sum to n terms and arithmetic mean.

• Geometric Progressions, their nth term, their sum to n terms and sum to infinite GP.

• Geometric mean and relationship between A.M. and G.M.

• Formulas for the following special sums.

 

LERNING OUTCOMES:

After studying this lesson student should know 

• The term sequence and series, arithmetic progression, arithmetic mean, geometric progression, geometric mean. 

• Students should be able to find the nth term and the sum to n terms of the A.P. and G.P. sequences. 

• Students should know the special types of sequences and should be able to find their nth term and sum to n terms.

RESOURCES

• NCERT Text Book,

• NCERT Exemplar Book of mathematics,

RESOURCE MATERIAL : 

Worksheets,  E-content, Basics and formulas from  (cbsemathematics.com)

KEY WORDS RELATED  TO SEQUENCE AND SERIES:

Sequence, Series, Arithmetic Sequence (A.P.), Geometric Sequence (G.P.), Term, First Term, Common Difference, Common Ratio, nth Term, General Term, Sum of n Terms, Finite Series, Infinite Series, Progression, Consecutive Terms, Constant Sequence, Arithmetic Mean (A.M.), Geometric Mean (G.M.) 

PROCEDURE :

Start the session by asking the questions related to the sequence and series, then ask the few questions about the arithmetic progression of 10^th level. Now introduce the topic step by step as follows.

TOPIC

Arithmetic Progression

Geometric Progression 

Introduction:  

Explain the term Sequence  and series and the difference between them. Explain the method of finding the terms from the nth term of the sequences.

Sequence : 

An arrangement of numbers in a definite order according to some rule is called a sequence. The terms of the sequence are denoted by t₁, t₂, t₃, t₄, ……….. or a₁, a₂, a₃, a₄, ………………….

Series : 

If the terms of a sequence are connected by plus (or minus) sign, is called a series.

Progression: 

A sequence following some definite rule is called a progression.

Arithmetic Progression: 

A sequence is called arithmetic progression if the difference of a term and its previous term is always same.

Example: 2, 4, 6, 10, 12, 14, ................

Example: 2 + 4 + 6 + 10 + 12 + 14 + ................

General Arithmetic Progression

General arithmetic progression, their first term, common difference, their nth term and their sum to n terms.

n^th term of sequence is   t_n = a + (n-1)d

Where common difference “d” is given by:  d = a_n – a_n-1

n^th terms of an AP from the end of the sequence is:   l – (n - 1)d,  

where l is the last term of the sequence.

Three terms in AP, four terms in AP and five terms in AP. Nth term from the end of the sequence, sum to n terms from the end of the sequence and Arithmetic Mean.

Sum of the first n terms of AP is 

Where "a" is the first term and "d" is the common difference of the given AP sequence.

Sum of the first n terms of an AP is 

Where "a" is the first term and "l" is the last term of the given AP sequence.

Sum of the first n terms from the end of the AP sequence is given by

 

GEOMETRIC PROGRESSION:

Now teacher will explain Geometric Progression, general GP sequence, their first term, their common ratio and the nth term of the GP.

G.P. SERIES:

A sequence of non-zero numbers is called a geometric progression (G.P.) if the ratio of the term and the term preceding to it is always a constant quantity.

A sequence a₁, a₂, a₃, a₄, ………a_n, a_n+1  is called geometric progression. 

If   is the common ratio of GP. Where :   

General Geometric Progression is  a, ar, ar², ar³, ……….., ar^n-1

First term = a, Second term = ar,  and so on and  r is the common ratio of GP

n^th term in GP is =  ar^n-1 

Sum of first n terms in GP is 

Sum to n terms of GP, sum of the terms of the infinite GP. Geometric Mean of the GP.

Sum of first n terms in GP is

General GP with infinite number of terms is of the following type

ar, ar², ar³, ……….., ar^n-1 .........∞

Sum to infinite terms of GP is given by

 

Relationship between Geometric Mean and Arithmetic Mean.

Special type of sequence method of finding their nth terms and sum to n terms.

Explanation of special types of formulas of following type and their implementation in the problems.

 

 

 

STUDENTS DELIVERABLES:

• Review questions given by the teacher. 

• Students should prepare the presentation individually or in groups on the formulas of finding the nth term and sum to n terms of the AP and GP sequences.  

• Solve NCERT problems with examples.

EXTENDED LEARNING:

Students can extend their learning in   through the Resource Centre Mathematics . Students can also find many interesting topics on mathematics at the site:   cbsemathematics.com

ASSESSMENT TECHNIQUES:

Assignment sheet will be given as home work at the end of the topic. Separate sheets which will include questions of logical thinking and Higher order thinking skills will be given to the above average students.

Class Test , Oral Test , worksheet and Assignments. can be made the part of assessment.
Re-test(s) will be conducted on the basis of the performance of the students in the test.

FEEDBACK:

All those students who performed well will be appreciated positively, and all those who can not perform up to the mark will again be given some important tips, guidance and  positive motivation to go through the topic again and then re-evaluated again. If possible then provision of remedial classes can be made for batter results.

THANKS FOR YOUR VISIT

PLEASE COMMENT BELOW