**Q) **If p^{th} term of an A.P. is q and q^{th} term is p, then prove that its n^{th} term is (p + q – n).

**Ans: **We know that n^{th} term of an A.P. = a + (n-1) d

Therefore, p^{th }term T_{p }= a + (p – 1) x d = q

Similarly, q^{th }term T_{q }= a + (q – 1) x d = p

By solving these two equations from each other, we get:

pd – qd = q – p

**d** **= -1**

Hence, value of a = q – (p – 1) (-1)

**a = p + q – 1 **

Hence, n^{th} term of this AP is = a + (n – 1) d

= (p + q – 1) + (n -1) (-1)

= p + q – 1 – n + 1

**= p + q – n ……………. Hence Proved**