Question

If the p^th term of an A.P. is q and the q^th term is p, prove that its n^th term is (p + q - n).

Answer 1

a_p = q => A + (p - 1) D = q ......(i)

& a_q = p => A + (q - 1) D = p

Solve (i) & (ii) to get D = - 1 & A = p + q - 1

So, a_n = A + (n - 1) D

a_n = (p + q - 1) + (n - 1) (-1) 

a_n = p + q - n.