The first and the last term of an A.P. are a and l . . .

Question : The first and the last term of an A.P. are a and l respectively. Show that the sum of nth term from the beginning and nth term from the end is a+l.

Doubt by Utkrisht

Solution : 

First Term = a

Last Term = l

nth term from the beginning of the AP
a_n=a+(n-1)d — (1)

nth term from the ending of the AP

a_n'=l-(n-1)d — (2)

Adding equation (1) and (2)

a_n+a_n'=a+(n-1)d+l-(n-1)d
a_n+a_n'=a+l

So, the sum of nth term from the beginning and nth term from the end is a+l.

Hence Proved.