Question

the sum of all odd integers between 2 and l00 divisible by 3.
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Answer 1

Answer:

The odd integers between 2 and 100 which is divisible by 3 are 3, 9, 15, ..., 99.  First and last odd integer between 2 and 100 which is divisible by 3 are 3 and 99 respectively.  First term of given sequence is a = 3.  And common difference of AP is d = a2 – a1 = 9 –3 = 6.  Let 99 is nth term of sequence 3, 9, 15, .………., 99.  ∴ a + (n – 1) d = 99. (∵ an = a + (n – 1) d)  ⇒ 3 + (n – 1)6 = 99 (∵ a = 3 & d = 6)  ⇒ 6(n – 1) = 99 – 3 = 96  ⇒ n – 1 = 96 6 966 = 16  ⇒ n = 16 + 1 = 17.  Now, sum of sequence 3, 9, 15, ………, 99 = n 2 n2[a + an] = 17 2 172 [3 + 99] (∵ n = 17, a = 3 & an = 99)  = 17 2 172 × 102 = 17 × 51 = 867.  Hence, the sum of all odd integers between 2 and 100 which are divisible by 3 is 867.Read more on Sarthaks.com - https://www.sarthaks.com/1109179/find-the-sum-of-all-odd-integers-between-2-and-100-which-are-divisible-by-3

Step-by-step explanation:

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