How Do You Prove the Summation Formula S_{n} = \frac{n}{2}(2a + L)?

[thomas49th]

Prove that
$$S_{n} = \frac{n}{2}(2a + L)$$ where L = a +(n-1)d


Can someone guide me through the proof please

Thx

 

[mathman]

The statement of the problem is confusing. However, the standard proof of summation of arithmetic progression is to take the terms in reverse order and add it to the original sum in direct order, term by term. All pairwise sums are the same, so the sum is the number of terms times one pairwise sum divided by 2.

This is 8th grade or earlier math.