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Find thesum of all 3 digit natural numbers, which are multiples of 11.

Answer» All 3-digit natural numbers, which are multiples of 11 are given as 110, 121, 132,…., 990.
This is an AP is which a = 110, d = 11 and l = 990.
Let the given AP contain n terms. Then,
`T_(n) = 990 rArr a + (n-1)d = 990 rArr 110 + (n-1) xx 11 = 990`
`rArr 99 + 11n = 990 rArr 11n = 891 rArr n = 81.`
`therefore "required sum" = (n)/(2) (a+l) = (81)/(2) xx (110 + 990)`
` = ((81)/(2) xx 1100) = 44550.`
Hence, the required sum is 44550.


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