Ex 5.3, 5 - Chapter 5 Class 10 Arithmetic Progressions

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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. Since last term is given, we can use formula Sn = 𝑛/2 (a + l) Here, a = 5 , l = 45 & Sn = Sum = 400 We need to find n Putting values in formula Sn = 𝑛/2 (a + l) 400 = 𝑛/2 (5 + 45) 400 = 𝑛/2 × 50 (400 × 2)/50 = n 8 × 2 = n 16 = n 8 × 2 = n 16 = n n = 16 So number of terms = 16 Now we need to find d For this we can use the formula Sn = 𝑛/2 (2a + n – 1) d) 400 = 16/2 (2 × 5 + (16 – 1)× d) 400 = 16/2 (10 + 15d) (400 × 2)/16 = 10 + 15d 50 = 10 + 15d 50 – 10 = 15d 40 = 15d 40/15 = d 8/3 = d d = 8/3