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

Question

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

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Answer

All even integers will have common differnce = 2 $\therefore$ A.P. is $102,\ 104,\ 106,\ ...,\ 998$ $\text{t}_\text{n}=\text{a}+(\text{n}-1)\text{d}$
$\text{t}_\text{n}=998,\text{a}=102,\text{d}=2$
$998=102+(\text{n}-1)(2)$
$998=102+2\text{n}-2$
$998-100=2\text{n}$
$2\text{n}=898$
$\text{n}=449$
$s_{449}$ can be calculated by $=\text{s}_\text{n}\frac{\text{n}}{2}[\text{a}+\text{l}]$
$=\frac{449}{2}[102+998]$
$=\frac{449}{2}[102+998]$
$=449\times550$
$=346950$

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