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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
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

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


Hence Proved.