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Question

The first and the last terms 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.


Solution

Given first term = a
Last term  = l
The nth term from starting
an=a+(n1)d   ...... (i)
The nth term from end
=l(n1)d   ...... (ii)
Adding (i) and (ii), we get
Sum of nth term from beginning and nth term from the end.
= a + (n - 1)d + l - (n - 1)d
= a + l

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