Question

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

Answer 1

Even integers between 101 and 999 are $102,104,10670,.......998$

Here,

$a=102,d=2,a_n=998$

By using the formula ,$a_n=a+(n-1)d$

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

$998-102=2(n-1)$

$896=2(n-1)$

$n=448+1$

$n=449$

By using the formula ,Sum of nth terms , $S_n=\frac{n}{2}[a+l]$

$\Rightarrow S_{449}=\frac{449}{2}(a+l)$

$\Rightarrow S_{449}=\frac{449}{2}(102+998)$

$\Rightarrow S_{449}=449\times 550=246950$