UPSC NDA Math Model Paper 1

Let the Arithmetic Progression consisting of n terms, with first term a and common difference d, be:
a,a+d,a+2d,a+3d,......a +(n−2)d,a+(n−1)d
Sum of first term and last term =a+a+(n−1)d=2a+nd−d
Sum of second term and second last term =a+d+a+(n−2)d =2a+nd−d.
And so on.
So, we can say that in an Arithmetic Progression, the sum of the terms equidistant from the beginning and the end is equal to the sum of the first and the last term.