What is the sum of the first 51 consecutive odd positive integers?

We call:

as the set of the first 51 consecutive odd positive integers, so:



Where:





and so on.

In mathematics, a sequence of numbers, such that the difference between two consecutive terms is constant, is called Arithmetic Progression, so:

3-1 = 2
5-3 = 2
7-5 = 2
9-7 = 2 and so on.

Then, the common difference is 2, thus:



Then:



So, we need to find the sum of the members of the finite series, which is called arithmetic series:

There is a formula for arithmetic series, namely:



Therefore, we need to find:
  

Given that , then:



Thus:


Lastly:

 

The answer to the question is d