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Ex 5.3, 8 - Find sum of first 51 terms of an AP whose second - Determining AP and finding sum

  1. Chapter 5 Class 10 Arithmetic Progressions
  2. Serial order wise
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Ex 5.3 ,8 Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively. We know that an = a + (n – 1) d From (1) & (2) 14 – d = 18 – 2d 2d – d = 18 – 14 d = 4 Putting value of d in (1) a = 14 – d a = 14 – 4 a = 10 Now, we need to find sum of first 51 terms We can use formula Sn = 𝑛/2 (2 a + (n – 1) d) Here , n = 51 , a = 10 & d = 4 Putting values Sn = 𝑛/2 (2a + (n – 1) d) S51 = 51/2 (2 ×10+(51−1)×4) S51 = 51/2 (20 + 50×4) S51 = 51/2×(20+200) S51 = 51/2×220 S51 = 51 × 110 S51 = 5610 Hence the sum of first 51 terms is 5610

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