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

The odd numbers between 0 and 50 are 1, 3, 5, 7, 9 … 49.

Therefore, we can see that these odd numbers are in the form of A.P.

Hence,
First term, a = 1
Common difference, d = 2
Last term, l = 49

By the formula of last term, we know,
$$l = a+(n-1) d$$
$$\Rightarrow 49 = 1+(n-1)2$$
$$\Rightarrow 48 = 2(n -1)$$
$$\Rightarrow n - 1 = 24$$
$$\Rightarrow$$ n = 25 = Number of terms

By the formula of sum of $$n^{th}$$ term, we know,

$$S_n = {{n} \over {2}}(a +l)$$
$$S_{25} = {{25} \over {2}} (1+49)$$
$$= {{25(50)} \over {2}}$$
$$=(25)(25)$$
$$= 625$$