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


Transcript

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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