Question

If the pth term of an AP is q and its qth term is p then show that its (p + q)th term is zero

Answer 1

In the given AP, let the first be a and the common difference be d.

Then , T_n  = a +(n-1) d 

⇒Tp = a+(p-1) d = q    ...............(1)

⇒T_q  = a + (q-1) d = p     ...........(2)

On subtracting (i) from (ii), we get:

(q-p) d= (p-q) 

⇒ d= -1

Putting d = - 1 in (i), we get:

a= (p+q -1)

Thus ,a = (p+q -1) and d = -1 

Now , T _p+q = a + (p+q-1)d

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

= (p+q-1)- (p+q-1) =0

Hence, the ( p+q)^th  term is 0 (zero).