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Lesson Plan, Class XI Ch-9 | Sequence and Series
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TEACHER'S NAME : ABC |
SCHOOL: XYZ |
SUBJECT : MATHEMATICS |
CLASS
: XI STANDARD BOARD
: CBSE |
LESSON TOPIC / TITLE: CHAPTER 09: SEQUENCE & SERIES |
ESTIMATED DURATION: This chapter is divided into 10 modules and is completed in 25 class meetings. |
- 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.
S. No. |
Topic |
1 |
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, …………………. Example: 2, 4, 6, 10, 12, 14, ................ Series : If the terms of a sequence are connected by plus (or minus) sign, is called a series.Example: 2 + 4 + 6 + 10 + 12 + 14 + ................ 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. |
2 |
General Arithmetic Progression General arithmetic
progression, their first term, common difference, their nth term and their
sum to n terms. nth term of sequence is tn = a + (n-1)d Where common difference “d” is given by: d = an – an-1 nth terms of an AP from the end of the sequence is: l – (n-1)d, where l is the last term of the sequence. |
3 |
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
|
4 |
GEOMETRIC PROGRESSION Now teacher will explain Geometric Progression,
general GP sequence, their first term, their common ratio and the nth term of
the GP. GP 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, ………an, an+1 is called geometric progression. If General Geometric Progression is a, ar, ar2, ar3, ……….., arn-1 First term = a, Second term = ar, and so on and r is the common ratio of GP nth term in GP is = arn-1
|
5 |
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 Sum of first n terms in GP is General GP with infinite number of terms is of the following type ar, ar2, ar3, ……….., arn-1 .........∞ Sum to infinite terms of GP is given by
|
6 |
Relationship between
Geometric Mean and Arithmetic Mean. |
7 |
Special type of
sequence method of finding their nth terms and sum to n terms. |
8 |
Explanation of special
types of formulas of following type and their implementation in the
problems. REFERENCES:- |
- 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.
- 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.
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Very nice
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