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Lesson Title Introduction to Arithematic Progression Subject :- Mathematics Class :- 10 th Time Required :- 35 to 40 minutes

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General Objectives To develop the mental ability of the students. To develop the logical reasoning of the Students.

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Specific Objectives Upon the completion of the lesson the students will be able to To determine the n th term of an Arithmetic Progression and give the examples thereof. To solve the problems related to n th term (General term) of an A.P.

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Skills to be developed 1. Self Expression 2. Co-relation of the topic / knowledge with daily life What mathematical skill(s) and understanding(s) will be developed? 3. Learning by experience /Doing

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Lesson Launch Exactly how will you use the first five minutes of the lesson? Teacher will take some examples related to daily life and put the students in a thinking situation. Say, like this A gardener buys a plant that is 10cm in height. Each week after that the plant grows 5cm. Note: The plant is 10cm high at the beginning of the first week. What will be the height of the plant at the beginning of the 1st, 2nd, 3rd, 4th and 5th weeks, if it follows the same pattern? 10cm 15cm 20cm 25cm 30cm

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Rs 2 Rs 4 Rs 6 Rs 8 - - - - - - - - - - Rs 14 If Pankaj saves Rs 2 daily from his pocket money. What would be the list / pattern of saved money each day during a week

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If Ramesh gets a loan of Rs. 1000/- from his friend with the condition that he will return the money in monthly installments of Rs 100/. What would be the Pattren / list of remaining loan money after each month. Rs 1000, 900, 800, 700, - - - - - - - - - - -, 100, 0

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Discussion Teacher will ask the students, “Is there any definite order in the list / pattern you have observed in the above examples ?” If the students are unable to answer, the teacher will tell about the pattern in example 1 and the students will work out the pattern in example 2 and 3.

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The teacher shall write the answers /patterns on the Board 10, 15, 20, 25, -- - - - - - - - - - - - - 2, 4, 6, 8, 10, 12, 14 1000, 900, 800, - - - - - - - - -, 100, 0 In example 1. you see that list of numbers is in a definite pattern. Here 10 is fisrt term, 2 nd term is obtained by adding 5, Similarly successive terms are obtained by adding 5 to the previous. Ask the student, “ what is the first term and that definite number which is added or subtracted from the previous term to get the successive term, in exampl 2 and 3 ?

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The students will probably give the following answers in ex. 2. First term is “2” and the definite number is “2” in ex. 3. First term is “1000” and the definite number is “-100” Thus we see that in these list of number each successive term is obtained by adding a definite number to the pervious term, such a list is called an A.P. At this point of time the teacher will dictate the definition of A.P.

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The first term is denoted by a 1, second by a 2, third by a 3, so on n th term by a n and the definite number is called the Common difference of the A.P. and is denoted by “d”. This common difference can be positive, negative or zero. Thus the A.P. is written as a 1, a 2,a 3, - - - - - - -,a n And d = a 2 - a 1 = a 3 – a 2 = a 4 – a 3 ………….., a n – a n-1

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Act in Group Divide the class in small groups of 4-5 students. Provide each group with a first term and a Common difference and tell them to form an A.P. Give them 2 or 3 minutes…. Have the students respond, and share some responses with the class ( responses may be written on the board)

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Now the teacher will give the idea of finite / infinite A.P. referring to example 1,2 and 3. given in the begining a = 5, d = 2, A.P. 5, 5+1(2), 5+2(2), 5+3(2), - - - - - - (example) a = 10, d = 3, A.P. 10, 10+3,10+6, 10+9, - - - - - a =-10, d = 2, A.P. -10, -10+2,-10+4, - - - - - - a = 15, d =-5, A.P. 15, 15+(-5), 15+(-10), 15+(-15) - - - - - - - - a = 100, d = 0, A.P. !00, !00+0, 100+0,- - - - - - - - - a = 10.5, d = 0.5, A. P. 10.5, !0.5+0.5, 10.5+2(0.5), 10.5+3(0.5), - - - - - - - - - Now in the context of above examples,by following the pattern the class shall reach upon a genral form of an A.P. a, a+d, a+2d, a+3d, a+4d, - - - - - - - - -

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Class Evaluation Can students generate examples of A.P. Are students able to identify A.P. A worksheet will be given to the students to solve within a time period of about 5 min What are my plans for tomorrow’s lesson based on the information I have gathered about student understanding in this lesson?

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Homework They may also be given to solve the textual exercise. Students are asked to form 5 examples of A.P. in situations of their daily life as assignment for the next day

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WORKSHEET ListIs it A.P. or notFirst term (a) Common Diff (d) Finite or Infinite 0, 2,4 6 8 - - - 60 Yes 0 2Finite 1, 3,5,7, - - - - 5,5,5,5, -- - - - 350, 300, 250,- - - 50 -3, -2, -1, - - - a, 2a,3a, - - - 3/2,1/2,-1/2, - - - 1,1,2,2,3,3,- - - - -3.1,-3.0,-2.9 - - - -2.0

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Prepared by Sh Pawan Kumar, Lect. Maths,GSSS Sihunta, Distt Chamba. Sh Bhim Singh, Lect. Maths,GSSS Drang, Distt. Mandi. Sh Dheeraj Vyas, Lect. Maths, GSSS khalet, Distt Kangra. Sh Om Prakash, T.G.T. (N/M,), GSSS Chandi, Distt Solan.

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