Find the sun of all odd numbers between 100 and 200. - Vidyadip

Question

Find the sun of all odd numbers between 100 and 200.

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Answer

The series so formed is 101, 103, 105, ... , 199
Let number of terms be n
then,
$\text{a}_\text{n}=\text{a}+(\text{n}-1)2$
$\Rightarrow199=101+(\text{n}-1)2$
$\Rightarrow\text{n}=50$
The sum of n terms $=\text{s}_\text{n}=\frac{\text{n}}{2}[\text{a}+\text{l}]$
$\text{s}_{50}=\frac{50}{2}[101+199]$
$=7500$
The sum of odd numbers between 100 and 200 is 7500.

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