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Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.

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Required numbers are 105,110,115,…., 995,
This is an AP in which a= 105, d= ( 110- 105) =5 and l = 995
` T_(n) = 995 Rightarrow a+( n-1) d= 995`
` Rightarrow 105 + (n-1) xx 5 = 995`
` Rightarrow (n-1) = 890/ 5 = 178 Rightarrow n = 179 `
` S_(n) = n/2 (a+l) = 179/2 xx ( 105 + 995) = ( 179/2 xx 1100)`
` ( 179 xx 550) = 98450`
Hence, the required sum is 98450

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