Find the sum of all integers between 101 and 500, which are divisible by 9.

To Find: Sum of all integers between 101 and 500 divisible by 9


The integers between 101 and 500 divisible by 9 are 108, 117, 126,…, 495(Add 9 to 108 to get 117, 9 to 117 to get 126 and so on).


Let a be the first term and d be the common difference and n be the number of terms of the AP


Here a = 108, d = 9, l = 495


a + (n - 1)d = 495


108 + 9(n - 1) = 495


12 + (n - 1) = 55


n = 55 - 11 = 44


Now,



S = 22[216 + 387] = 22[603] = 13266


Sum of all integers divisible by 9 between 100 and 500 is 13266.


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