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

The sum of the first n terms of an AP is given by Sₙ = n/2 [2a + (n - 1) d] or Sₙ = n/2 [a + l].

Here, a is the first term, 

d is a common difference and 

n is the number of terms.

The odd numbers lying between 0 and 50 are 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, ...,45, 47, 49

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

Hence,

First-term, a = 1

Common difference, d = 2

Last term, l = 49

We know that nth term of AP, aₙ = l = a + (n - 1)d

49 = 1 + (n - 1) 2

48 = 2(n - 1)

n - 1 = 24

n = 25

We know that sum of n terms of AP,

Sₙ = n/2 [a + l]

S₂₅ = 25/2 (1 + 49)

= 25/2 × 50

= 25 × 25

= 625

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

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