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

Question:

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

Solution:

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.

$198=102+(n-1) 2$

$\Rightarrow 96=(n-1) 2$

$\Rightarrow 48=n-1$

$\Rightarrow n=49$

Now, $S=\frac{49}{2}[102+198]=49 \times 150=7350$

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