Ex 5.3, 9 - If sum of first 7 terms of an AP is 49 - Determining AP and finding sum

  1. Chapter 5 Class 10 Arithmetic Progressions
  2. Serial order wise
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Ex 5.3 ,9 If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first n terms. We know that Sn = ๐‘›/2 (2๐‘Ž+(๐‘›โˆ’1)๐‘‘) From (1) and (2) 7 โ€“ 3d = 17 โ€“ 8d 8d โ€“ 3d = 17 โ€“ 7 5d = 10 d = 10/5 d = 2 Putting value of d in (1) a = 7 โ€“ 3d a = 7 โ€“ 3 ร—2 a = 7 โ€“ 6 a = 1 Hence, a = 1 & d = 2 We need to find sum of first n terms We can use formula Sn = ๐‘›/2 (2a + (n โ€“ 1) d) = ๐‘›/2 (2 ร—1+(๐‘›โˆ’1)2) = ๐‘›/2(2+2๐‘›โˆ’2) = ๐‘›/2 (0 + 2n) = ๐‘›/2ร—2๐‘› = n2

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