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## Answers

l=a+(n-1)d

49=1+(n-1)2

2n-2=48

2n=50

n=50/2

n=25

Sn=n/2(a+l)

=25/2(1+49)

=25/2(50)

=25(25)

=625.

Therefore the sum of all odd numbers between 0 and 50 is 625.

Let,

sum = 1 + 3 + 5 + 7 + ......+49.

this is an A.P, whose first term(a) = 1 and last term(Tn) = 49.

common difference(d) = 3-1 = 2

Total no. of odd number lie b/w 0 and 50 = n

but,

Tn = a + (n-1)d

or, 49 = 1 + (n-1)2

or, n-1 = 48/2 =24

n = 25

hence

sum = n/2(a + Tn)

sum = 25(1 + 49)/2

sum = 25×50/2 = 25×25

sum = 625