Find the sum of integers from 1 to 100 that are divisible by 2 or 5.

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The integers from 1 to 100, which are divisible by 2, are 2, 4, 6… 100. This forms an A.P. with both the first term and common difference equal to 2. ⇒100 = 2 + (n –1) 2 ⇒ n = 50 The integers from 1 to 100, which are divisible by 5, are 5, 10… 100. This forms an A.P. with...
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The integers from 1 to 100, which are divisible by 2, are 2, 4, 6… 100. This forms an A.P. with both the first term and common difference equal to 2. ⇒100 = 2 + (n–1) 2 ⇒n= 50 The integers from 1 to 100, which are divisible by 5, are 5, 10… 100. This forms an A.P. with both the first term and common difference equal to 5. ∴100 = 5 + (n–1) 5 ⇒ 5n= 100 ⇒n= 20 The integers, which are divisible by both 2 and 5, are 10, 20, … 100. This also forms an A.P. with both the first term and common difference equal to 10. ∴100 = 10 + (n–1) (10) ⇒ 100 = 10n ⇒n= 10 ∴Required sum = 2550 + 1050 – 550 = 3050 Thus, the sum of the integers from 1 to 100, which are divisible by 2 or 5, is 3050. read less
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