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

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

So,

pth term =a+(p-1)d = q

qth term =a+(q-1)d = p

Acc to qn

p[a+(p-1)d] = q[a+(q-1)d] (Finding ratio of two terms and cross multiplying)

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.