We know that the sum of an arithmetic series would be like this:
The first term is represented as a, the common difference is d and the last term is represented as L. If we add the first term and the last term, we get:
If we add the second term with the second last term, we get:
If we add the third term with the third last term we get:
If we do the same with the fourth term, the fifth term, the sixth term and so on, we will always end up with [a + L], now lets say Sn is equal to the sum of an arithmetic series where n is the number of terms. Suppose we write Sn in the proper order and in the reverse order:
If we add them, we get:
Since [a + L] repeats n times, we can simplify this:
Instead of using L for the last term, we can write:
If we simplify, we get:
