Sir please give me a detailed solution of this question in which we have given a and l are the first and last term of an AP and we have to prove that sum of nth term from the beginning and the nth term from the end is (a + l).

Book RS Aggarwal, class 10, chapter 5A, question no 41

## a1=a

Let

ak=l

a+(k−1)d=l

d=(l−a)/(k-1)

nth term from beginning =an

=a+(n−1)d=a+(n−1)(l−a)/(k-1)

nth term from end =l+(n−1)(−d)=l−(n−1)(l−a)/(k-1)

Sum of nth terms from beginning and from end =a+(n−1)(l−a)/(k-1) +l−(n−1)(l−a)/(k-1)=a+l

proved.