Show that the sum of an AP whose first term is a, the second term b and the last term c, is equal to

Given that, the AP is a, b, …, c.

Here, first term = a

common difference = b - a

and last term, a_n = c

as nth term of an AP

a_n = a + (n - 1)d

[ eqn 1]

Sum of an AP

So

Hence Proved.