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 Find the sum of all natural numbers between 100 to 200 and which are not divisible by 4 . [ Calculator, Method and examples ]Solution:Your problem -> Find the sum of all natural numbers between 100 to 200 and which are not divisible by 4 .Required Addition = (100 + 101 + 102... + 200) - (100 + 104 + 108... + 200)Required Addition = S' - S''We know that, S_n = n/2 (a + l):. S_101 = 101/2 * (100 + 200)= 101/2 (300)= 15150Numbers between 100 and 200 divisible by 4 are 100, 104, 108 ...Which are in arithmetic progression.In which a=100 and d=4Let n be the term such that f(n) = 200We know that, f(n) = a + (n - 1)d100 + (n - 1)(4) = 200(n - 1)(4) = 100n - 1 = 25n = 26We know that, S_n = n/2 [2a + (n - 1)d]:. S_26 = 26/2 * [2(100) + (26 - 1)(4)]= 13 * [200 + (100)]= 13 * [300]= 3900:. Required Addition = 15150 - 3900= 11250

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