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.

If p times the pth term  and q times the qth term  of an A.P are equal, then prove thatits (p+q)th term is zero.

 

Soln.

Let a and d be respetively the first term and the common diff of the A.P.

So,

pth term =a+(p-1)d

qth term =a+(q-1)d

Acc to qn

p[a+(p-1)d]=q[a+(q-1)d]

So,

a(p-q)+d[p(p-1)-q(q-1)]=0

a(p-q)+d[{(p+q)(p-q)-(p-q)]=0

(p-q)[a+d{(p+q)-1}=0

since p is not equal to q,so p-q can't b equal to zero.

so

a+d{(p+q)-1]=0

thus the (p+q)th term is equal to zero.

 

pl chk the qn which you have given again. However we have solved another question of similar type for you.