Question

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 form the end is (a + l).

Answer 1

In the given AP, first term = a and last term = l.

Let the common difference be d.

Then, nth term from the beginning is given by

T_n = a + (n – 1)d   ...(1)

Similarly, nth 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 nth term from the beginning and the nth term from the end (a + l).