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
an=a+(n-1)d — (1)
an=a+(n-1)d — (1)
nth term from the ending of the AP
an'=l-(n-1)d — (2)
Adding equation (1) and (2)
an+an'=a+(n-1)d+l-(n-1)d
an+an'=a+l
an+an'=a+l
So, the sum of nth term from the beginning and nth term from the end is a+l.
Hence Proved.