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Ex 5.3, 5 - The first term of an AP is 5, last term is 45, sum is 400

Ex 5.3, 5 - Chapter 5 Class 10 Arithmetic Progressions - Part 2
Ex 5.3, 5 - Chapter 5 Class 10 Arithmetic Progressions - Part 3

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Ex 5.3, 5 The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference. Given a = 5 , l = 45 & Sn = Sum = 400 Since last term is given, we can use formula Sn = š’/šŸ (a + l) Putting values in formula 400 = š‘›/2 (5 + 45) 400 = š‘›/2 Ɨ 50 (400 Ɨ 2)/50 = n 8 Ɨ 2 = n 16 = n n = 16 So, Number of terms = 16 Finding d For d, we use the formula Sn = š’/šŸ (2a + n ā€“ 1) d) Putting Sn = 400, n = 16, a = 5 400 = 16/2 (2 Ɨ 5 + (16 ā€“ 1)Ɨ d) 400 = 8 Ɨ (10 + 15d) 400/8 = 10 + 15d 50 = 10 + 15d 50 ā€“ 10 = 15d 40 = 15d 40/15 = d 8/3 = d d = šŸ–/šŸ‘

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