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

Question

Philoid · Accepted Answer

Odd numbers from 0 to 50 are 1, 3, 5, …, 49

Sum of these numbers is 1 + 3 + 5 + … + 49.

This forms an Arithmetic Series with first term = a = 1

and Common Difference = d = 3 - 1 = 2

There are 25 terms in this Arithmetic Series.

Now, sum of n terms is given as:

S_n = (n/2)[2a + (n - 1)d]

S₂₅ = (25/2)[2(1) + (25 - 1)2]

= (25/2)[2 + 48]

= (25 × 50)/2

= 25 × 25

= 625

∴ Sum of odd numbers from 0 to 50 is 625.