If the pth term of an AP is q and the qth term is p, prove that its nth term is (p+q-n).

Answer 1

a+(p-1)d = q
a+(q-1)d = p

(p-1)d-q = (q-1)d-p
[(p-1)-(q-1)]d = q-p
(p-q)d = q-p
d = (q-p)/(p-q) = -1

Tn = Tq + (n-q)d
= p + (n-q)(-1)
= p+q-n

Answer 2

thnaks :)