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).

Question

Philoid · Accepted Answer

Let d be the common difference of the AP.

First term = a

Last term = l = 1

n^th term from beginning of an AP is given by:

a_n = a + (n - 1)d …………………………….(1)

n^th term from the end of an AP is given by:

T_n = l - (n - 1)d

= 1 - (n - 1)d …………………………….(2)

Sum of the n^th term from the beginning and end is given by:

a_n + T_n = a + (n - 1)d + 1 - (n - 1)d

= a + 1

Hence, proved.