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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 = 𝒏/𝟐 (a + l) Putting values in formula 400 = 𝑛/2 (5 + 45) 400 = 𝑛/2 Γ— 50 (400 Γ— 2)/50 = n 8 Γ— 2 = n 16 = n n = 16 So, Number of terms = 16 Finding d For d, we use the formula Sn = 𝒏/𝟐 (2a + n – 1) d) Putting Sn = 400, n = 16, a = 5 400 = 16/2 (2 Γ— 5 + (16 – 1)Γ— d) 400 = 8 Γ— (10 + 15d) 400/8 = 10 + 15d 50 = 10 + 15d 50 – 10 = 15d 40 = 15d 40/15 = d 8/3 = d d = πŸ–/πŸ‘

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.