The first and last terms of an AP are a and l, respectively. Show that the sum of the nth term from the beginning and the nth term from the end is (a + 1).

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Solution

In the given AP, first term = a and last term = l.
Let the common difference be d.
Then, n^th term from the beginning is given by
T_n = a + (n - 1)d ...(1)

Similarly, n^th term from the end is given by
T_n = {l - (n - 1)d} ...(2)
Adding (1) and (2), we get:
a + (n - 1)d + {l - (n - 1)d}
= a + (n - 1)d + l - (n - 1)d
= a + l

Hence, the sum of the n^th term from the beginning and the n^th term from the end is (a + l) .

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