Find the sum of integers between 2 and 500 divisible by 2 or 5

1.	Find the sum of integers between 2 and 500 divisible by 2 or 5
Answer» Integers between 2\xa0and 500 which are multiples of 2 as well as 5 are10, 20, 30,............, 490This forms an A.P. with a = 10, d = 10, and l = 490Let the number of these terms be n.Then,an\xa0= 490{tex}\\Rightarrow{/tex}a + (n - 1)d = 490{tex}\\Rightarrow{/tex}10 + (n - 1)(10) = 490{tex}\\Rightarrow{/tex}(n - 1)(10) = 480{tex}\\Rightarrow{/tex}n - 1 = 48{tex}\\Rightarrow{/tex}\xa0n = 49{tex}\\Rightarrow S _ { 49 } = \\frac { 49 } { 2 } [ 2 \\times 10 + 48 \\times 10 ]{/tex}{tex}= \\frac { 49 } { 2 } \\times [ 20 + 480 ]{/tex}{tex}= \\frac { 49 } { 2 } \\times 500{/tex}= 12250

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