Q. 124.5( 8 Votes )

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

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:


Sn = (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.


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