Question

Find the sum of all integers between 100 and 600, each of which when divided by 5 leaves 2 as remainder.

Answer 1

The integers between 100 and 600 divisible by 5 and leaves remainder 2 are 102, 107, 112, 117,…, 597.

To Find: Sum of the above AP

Here a = 102, d = 5, l = 597

a + (n - 1)d = 597

⇒102 + 5(n - 1) = 597

⇒ (n - 1) = 99

⇒ n = 100

⇒ S = 50[204 + 495] = 50 × 699 = 34950

The sum of all such integers is 34950.