Q1.If the pth term of an AP is equal to q and qth term is equal to p.Then prove that the nth term is p+q-1.

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

Given : p ^th term = q

? a + (p – 1) d = q ..... (1)

and g ^th term = p

? a + (q – 1) d = p ...... (2)

Subtracting (2) term (1), we get

(p – q)d = (q – p)

d = 1

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

a + (p – 1) (– 1) = q

? a = p + q – 1

 ? n ^th term = a + (n – 1) d = (p + q – 1) + (n – 1) (– 1)

= p + q – 1 – n + 1 = p + q – n

 ? n ^th term of the given A. P. is (p + q – n)