CBSEi Class 10 Sequences (AP and GP) CORE

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Thus, the sum of first n terms of an AP is given by Sn = [2a + (n 1) d] Note that last term of the AP = = a+(n 1) d. Let = a + (n 1) d. So, , = [2a + (n 1) d] = [a + a + (n 1) d] = [a + ] Hence = [a+ ], where is the last term or nth term. The above method is similar to the one used by the great German mathematician Carl friedrich Gauss (1777-1855) when he was in elementary school. His teacher asked the class to find the sum of first 100 natural numbers. Gauss found the sum as follows: 1 + 2 + 3 + 4 + ………… + 98 + 99 + 100 100 + 99 + 98 + 97 + ……….... + 3 + 2 + 1 101 + 101 + 101 + 101 + ………… + 101 + 101 + 101 101, 100 times i.e., sum = = 5050 61
Example 23: find the sum of first (i) 100 natural numbers. (ii) 1000 natural numbers. Solution: (i) Here a=1, d=1, n = 100 Thus, S100 = [2x1 + (100-1) 1] = 50x 101 = 5050 Alternatively, we may use the formula Sn = (a + ) S100 = (1+100) = 5050 (ii) Using the formula for Sn, S1000 = [2 x 1 + (1000 1 1] = 500 (1001) = 500500 Also by using the formula : Sn = (a+ ) S1000 = (1 + 1000) = 500 (1001) = 500500 Example 24: Find the sum of first 50 terms of the AP; 1, 3, 5, 7,……….. Solution: Here a=1, d=2, n=50 using the formula 62
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CBSE-i Mathematics Arithmetic Progr
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The CBSE-International is grateful
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ACKNOWLEDGEMENTS Advisory Conceptua
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CContent Worksheet CW7 22 General T
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Introduction to Arithmetic Syllabus
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Mozart the finest musician of the w
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Teacher’s Note The teaching of Ma
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ealise that if general term is give
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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 56 and 57: - = = = = Thus, it is not an AP (Wh
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 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,
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Page 102 and 103: Student’s Worksheet 10 Content Wo
Page 104 and 105: Step 6 Take the strip of dimension
Page 106 and 107: Parameters of assessment Self Asses
Page 108 and 109: a 3. Take the suitable value for fi
Page 114 and 115: 5. Find a G.P. whose 3 rd and 6 th
Page 118 and 119: 5. Visit the link http://betterexpl
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Student’s Worksheet 15 Content Wo
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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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