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

Let d be the common difference of the AP.

First term = a

Last term = l = 1

nth term from beginning of an AP is given by:

an = a + (n - 1)d …………………………….(1)

nth term from the end of an AP is given by:

Tn = l - (n - 1)d

= 1 - (n - 1)d …………………………….(2)

Sum of the nth term from the beginning and end is given by:

an + Tn = a + (n - 1)d + 1 - (n - 1)d

= a + 1

Hence, proved.

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