Find the sum of the odd numbers between 0 and 50.

Solution:

1, 3, 5, 7 ..., 49

a = 1, d = 2

$\ell=\mathrm{t}_{\mathrm{n}}=49$

$\Rightarrow a+(n-1) d=49$

$\Rightarrow 1+(n-1)(2)=49$

$\Rightarrow 1+2 n-2=49$

$\Rightarrow 2 n=50$ or $n=25$

The sum $=\frac{25}{2}\{a+\ell\}=\frac{25}{2}\{1+49)$

$=\frac{25}{2} \times 50=625$