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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