Question

Find the sum of all even integers between 101 and 199.

Answer 1

To Find: The sum of all even integers between 101 and 199.

The even integers form the following AP series -

102, 104, …, 198

It is and AP series with a = 102 and l = 198.

198 = 102 + (n - 1)2

⇒ 96 = (n - 1)2

⇒ 48 = n – 1

⇒ n = 49

Now, S = 49/2[102+198] = 49 x 150 = 7350

The sum of all even integers between 101 and 199 is 7350.