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.