Question

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

Answer 1

The odd numbers between 0 and 50 are

1, 3, 5, 7, 9 ... 49

Therefore, it can be observed that these odd numbers are in an A.P.

a = 1

d = 2

l = 49

l = a + (n – 1) d

49 = 1 + (n – 1)2

48 = 2(n – 1)

n – 1 = 24

n = 25

`S_n = n/2(a + 1)`

`S_25 = 25/2(1 + 49)`

= `25/2 [50]`

= 25 × 25 

= 625

Thus, the sum of odd numbers between 0 and 50 is 625.