Question

OBJECTIVE :To find the sum of first n natural numbers. MATERIAL REQUIRED: Cardboard, coloured papers, white paper, cutter, adhesive. METHOD OF CONSTRUCTION : Take a rectangular cardboard of a convenient size and paste a coloured paper on it. Draw a rectangle ABCD of length 11 units and breadth 10 units. Divide this rectangle into unit squares as shown in Fig. 1. 3. Starting from upper left-most corner, colour one square, 2 squares and so on as shown in the figure. DEMONSTRATION : The pink colour region looks like a stair case. Length of 1st stair is 1 unit, length of 2nd stair is 2 units, length of 3rd stair 3 units, and so on, length of 10th stair is 10 units. These lengths give a pattern 1, 2, 3, 4, ..., 10, which is an AP with first term 1 and common difference 1. Sum of first ten terms = 1 + 2 + 3 + ... +10 = 55 ……………….. eq(1) Area of the shaded region = 1/ 2 (area of rectangle ABCD) = ½ ( length * breadth) =………………………. which is same as obtained in (1) above. This can be generalised to find the sum of first n natural numbers as Sn = 1/2×n(n+1) OBSERVATION: For n = 4, Sn = .............................. For n = 12, Sn = .............................. For n = 50, Sn = .............................. For n = 100, Sn = ............................. APPLICATION : Result (2) may be used to find the sum of first n terms of the list of numbers: 12 , 22 , 32 , ... 13 , 23 , 33 , ... PLS HELP I HV AN EXAM TOMORROW

Answer 1

Answer:

100

Step-by-step explanation:

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Answer 2

Answer:

100

Step-by-step explanation:

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