CBSEi Class 10 Sequences (AP and GP) CORE

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– = = = = Thus, it is not an AP (Why?) [Note that denominators 7, 9, 11, 13,…. are in AP, check!!] (v) 1, 1.7, 2.4, 3.1,…. We have, 1.7 – 1 = 0.7 2.4 – 1.7 = 0.7 3.1 – 2.4 = 0.7 So, it is an AP with common difference (d) = 0.7 (vi) 1 2, 5 2, 7 2, 73,…. 1 2, = 1, 5 2 = 25, 7 2 = 49, 73 =73. Further, 25 1 = 24 49 25 = 24 73 – 49 = 24 So, 1 2 , 5 2 , 7 2 , 73,…. is an AP with common difference (d) = 24 Example 5: Find the value of k for which k+2, 4k 6 and 3k 2 form three consecutive terms of an AP. Solution: a = k+2, a+d = 4k 6, a+2d = 3k 2, where d is the common difference. If k+2, 4k 6, 3k 2 are in AP, then d = (a+d) a = (4k 6) (k+2) = 3k 8 (1) Also, d = (a+2d) (a+d) = (3k 2) – (4k 6) = 4 k (2) 47
From (1) and (2), 3k 8 = 4 k or, k = 3. Thus, for k=3, the given three terms will form an AP. Example 6: Find AP whose first term is —2 and common difference is —5. Solution: Here a = 2, d = 5 So, the required AP will be a, a+d, a+2d,…… or 2, 2+( 5), 2 + 2( 5),…. or, 2, 7, 12,….. General Term of an AP Recall that if a is the first term and d is the common difference, then the AP is written as a, a+d, a+2d, …. Note that first term( ) = a = a + (1 1) d second term ( ) = a + d = a + (2 1) d third term ( ) = a + 2d = a + (3 1) d fourth term ( ) = a + 3d = a + (4 1) d ……. tenth term ( ) = a + 9d = a + (10 – 1) d 50 th term ( ) = a + 49d = a + (50 – 1) d Observing the pattern (coefficient of d in any term is 1 less than the term number), we can write nth term ( )= a + (n 1) d = a + (n 1) d 48
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CBSE-i Mathematics Arithmetic Progr
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The CBSE-International is grateful
Page 6 and 7: ACKNOWLEDGEMENTS Advisory Conceptua
Page 8 and 9: CContent Worksheet CW7 22 General T
Page 10 and 11: Introduction to Arithmetic Syllabus
Page 12 and 13: Mozart the finest musician of the w
Page 14 and 15: Teacher’s Note The teaching of Ma
Page 16 and 17: ealise that if general term is give
Page 18 and 19: Activity skill Matrix Activity Skil
Page 20 and 21: Activity 1 - Warm Up (W1) Recognisi
Page 22 and 23: Activity 3 - Warm Up (W3) Designs a
Page 24 and 25: Activity 5 - Pre Content (P2) Visua
Page 26 and 27: Activity 7 - Content (CW2) Recognis
Page 28 and 29: Activity 9 - Content (CW4) Problems
Page 30 and 31: Specific objective: To recognise a
Page 32 and 33: Activity 13 - Content (CW8) Problem
Page 34 and 35: Activity 15 - Content (CW10) Hands
Page 36 and 37: Activity 17 - Post Content (PCW1) A
Page 38 and 39: Able to write general term when any
Page 40 and 41: Teachers’ Rubric for Summative As
Page 42 and 43: Able to find the sum of given numbe
Page 44 and 45: STUDY MATERIAL 35
Page 46 and 47: (v) (vi) Area of 3 rd square = = ,
Page 48 and 49: (vi) Area of fourth square = Simila
Page 50 and 51: (iii) 1, 2, 4, 8, ______________ (i
Page 52 and 53: (ii) 54 = 54 18 = = 54 3 6 = = 18 3
Page 54 and 55: The fixed number is called the comm
Page 58 and 59: is called the general term of an AP
Page 60 and 61: or, 185 = 40 + 25n 25 or, 25n = 250
Page 62 and 63: The fixed number is called the comm
Page 64 and 65: Here a = 2 6 ( 2) = 3 18 ( 6) = 3 5
Page 66 and 67: Example 18 : Find 8 th term of the
Page 68 and 69: or, = or, a = = i.e., the first ter
Page 70 and 71: Thus, the sum of first n terms of a
Page 72 and 73: Sn = [2a + (n 1)d] S50 = [2x1 + (50
Page 74 and 75: Example 28: The sum of first 22 ter
Page 76 and 77: Student’s Worksheet 1 Warm up (W1
Page 82 and 83: Student’s Worksheet 4 Pre Content
Page 84 and 85: Student’s Worksheet 5 Pre Content
Page 86 and 87: Student’s Worksheet 6 Content Wor
Page 88 and 89: Parameters of assessment Self Asses
Page 90 and 91: 2. Investigation : For which of the
Page 94 and 95: 2. Which of the following expressio
Page 98 and 99: 5. Given a sequence 6, 11, 16, 21,
Page 100 and 101: 11. 12. Can Can 91
Page 102 and 103: Student’s Worksheet 10 Content Wo
Page 104 and 105: Step 6 Take the strip of dimension
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Parameters of assessment Self Asses
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a 3. Take the suitable value for fi
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Student’s Worksheet 12 Content Wo
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5. Find a G.P. whose 3 rd and 6 th
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5. Visit the link http://betterexpl
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Self Assessment Rubric 15 Content W
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3. Find the sum of first n odd natu
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9. Find the sum of all odd integers
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PCW1 (Assignment) : Post Content Wo
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5. General term of an A.P. is alway
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PCW4 Framing questions Using the gi
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PCW5 Hands on activity Aim: To veri
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Suggested videos and Extra readings
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CBSEi Class 10 Sequences (AP and GP) CORE

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