Let a is the first term, d is the common ratio and l is the last term of the AP

Now n^th term of the series = a + (n - 1)d

Since n^th term is the last term of the series,

So, l =  a + (n - 1)d

Now, sum of n terms of the series S_n = (n/2)*{2a + (n - 1)d}

=> S_n = (n/2)*{a + a + (n - 1)d}

=> S_n = (n/2)*(a + l)

This the required relation between nth term and sum to nth terms of the AP