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Find the sum of all odd numbers between 0 and 50.
Given:
To do:
We have to find the sum of all
Solution:
Odd numbers between 0 and 50 are \( 1,3,5,7, \ldots, 49 \).
The sequence is in A.P.
Here,
\( a=1 \) and \( d=3-1=2 \) \( l=49 \)
We know that,
$l=a+(n-1) d$
$\Rightarrow 49=1+(n-1) \times 2$
$\Rightarrow 49=1+2 n-2$
$\Rightarrow 49+1=2 n$
$\Rightarrow n=\frac{50}{2}=25$
$\therefore n=25$
We know that,
$\mathrm{S}_{n}=\frac{n}{2}[2 a+(n-1) d]$
$=\frac{25}{2}[2 \times 1+(25-1) \times 2]$
$=\frac{25}{2}[2+24 \times 2]$
$=\frac{25}{2}(50)$
$=25 \times 25$
$=625$
The sum of all odd numbers between 0 and 50 is $625$.
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