Ex 5.3, 10 - Show that a1, a2, ... an form an AP where an

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

 

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Ex 5.3, 10 Show that a1, a2 … , an , … form an AP where an is defined as below (i) an = 3 + 4n .Also find the sum of first 15 terms an = 3 + 4n Taking n = 1 a1 = 3 + 4 × 1 a = 3 + 4 a = 7 Taking n = 2 a2 = 3 + 4 × 2 a2 = 3 + 8 a2 = 11 Taking n = 3 a3 = 3 + 4 × 3 a3 = 3 + 12 a3 = 15 Now we have to find sum of first 15 terms i.e. S15 We know that Sn = 𝑛/2 (2𝑎+(𝑛−1)𝑑) Here, n = 15, a = 7, d = 4 Putting the values S15 = 15/2 (2 ×7+(15−1)×4) = 15/2 (14 + 14 × 4) = 15/2 (14+46) = 15/2×70 = 15 × 35 = 525 Hence series is 7, 11, 15, ….. Since difference is same, it is an AP Common difference = d = 4

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo