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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 nthterm from the beginning and nth term from the end is a + l.
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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 = \[l + (n - 1)( - d) = l - dn + d\]
Their sum = \[a + (n - 1)d + l - dn + d\]
\[= a + nd - d + l - nd + d \]
\[ = a + l\]
Hence, proved.
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