Question

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

Answer 1

Let a be the first term and d be the common difference of the given A.P. Then,

p^th term = q ⇒ a + (p – 1) d = q ….(i)

q^th term = p ⇒ a + (q – 1) d = p ….(ii)

Subtracting equation (ii) from equation (i),

we get

(p – q) d = (q – p) ⇒ d = – 1

Putting d = – 1 in equation (i), we get

a = (p + q – 1)

n^th term = a + (n – 1) d

= (p + q – 1) + (n – 1) × (–1) = (p + q – n)