Question

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

pth term = q

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

qth term = p

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

Solving these equations, we get,

$d=-1$

$a=(p+q-1)$

Thus,

nth term = $a+(n-1)d=(p+q-1)+(n-1)\times (-1)=(p+q-n)$