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Find the sum of the odd numbers between 0 and 50.
Given:
To do:
We have to find the sum of the
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,
$l=a+(n-1) d$
$49=1+(n-1) \times 2$
$49=1+2 n-2$
$49+1=2 n$
$n=\frac{50}{2}=25$
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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