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.