Find the sum of all even integers between 101 and 999.

Question:

Find the sum of all even integers between 101 and 999.

Solution:

The even integers between 101 and 999 are:

102, 104...998

Here, we have:

$a=102$

$d=2$

$a_{n}=998$

$\Rightarrow 102+(n-1) 2=998$

$\Rightarrow 2 n-2=896$

$\Rightarrow 2 n=898$

$\Rightarrow n=449$

$S_{n}=\frac{n}{2}[2 a+(n-1) d]$

$\Rightarrow S_{449}=\frac{449}{2}[2 \times 102+(449-1) \times 2]$

$\Rightarrow S_{449}=\frac{449}{2}[1100]$

$\Rightarrow S_{449}=246950$

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