Question

Find sum of all odd numbers between 0 and 50

Answer 1

Odd number between 0 and 50 are 1,3,5,7,9.....49
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.

Answer 2

To find the sum of all odd numbers between 0 and 50. we will use the concept of arithmetic progression(A.P) .

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