Last updated at March 22, 2021 by Teachoo
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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+(๐โ1)๐) Sum of first 7 terms = 49 S7 = 7/2 (2๐+(๐โ1)๐) 49 = 7/2 (2๐+(7โ1)๐) 49 = 7/2 (2๐+6๐) (49 ร 2)/7 "= 2a + 6d" "14 = 2a + 6d" (14 โ 6๐)/2=๐ a = 7 โ 3d Sum of first 17 terms = 289 S17 = 17/2 (2๐+(17โ1)๐) 289 = 17/2 (2a + (17 โ 1) d) 289 = 17/2 (2a + 16d) (289 ร 2)/17 = 2a + 16d 34 = 2a + 16 d (34 โ 16๐)/2 = a a = 17 โ 8d 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 ร2 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 = ๐/๐ (2a + (n โ 1) d) Putting a = 1 & d = 2 = ๐/2 (2 ร 1+(๐โ1)2) = ๐/2(2+2๐โ2) = ๐/2 (0 + 2n) = ๐/2 ร 2n = n2
Ex 5.3
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