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 = { l- (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+1 

Hence, the sum of the nth term from the beginning and the nth term from the end (a +1).