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

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

nth term from the beginning $=a+(n-1) d$, where $d$ is the common difference.

nth term from the end $=l+(n-1)(-d)=l-d n+d$

Their sum $=a+(n-1) d+l-d n+d$

$=a+n d-d+l-n d+d$

$=a+n d-d+l-n d+d$

$=a+l$

Hence, proved.

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