Question:
Find the sum of all odd numbers between 100 and 200.
Solution:
All the odd numbers between 100 and 200 are:
101, 103...199
Here, we have:
$a=101$
$d=2$
$a_{n}=199$
$\Rightarrow 101+(n-1) \times 2=199$
$\Rightarrow 2 n-2=98$
$\Rightarrow 2 n=100$
$\Rightarrow n=50$
$S_{n}=\frac{n}{2}[2 a+(n-1) d]$
$\Rightarrow S_{50}=\frac{50}{2}[2 \times 101+(50-1) 2]$
$\Rightarrow S_{50}=25[202+98]$
$\Rightarrow S_{50}=7500$
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