Question

In an AP if p term is 1/q and q term is 1/p, then find the pq term..??​

Answer 1

Answer:

1

Explanation:

pth term-1/q

means....a+(p-1)d=1/q-------1

and

qth term-1/p

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

subtract eq 1 by 2

you will get..

(p-1)d-(q-1)d=1/q-1/p

dp-d-dq+d=p-q/pq

dp-dq=p-q/pq

d(p-q)=p-q/pq

d=1/pq

put value of d in eq 1

a+(p-1)1/pq=1/q

apq+p-1=p

apq=p-p+1

apq=1

a=1/pq

.....

therefore

tpq=a+(pq-1)d

=1/pq+(pq-1)1/pq

=1/pq+pq-1/pq

=1+pq-1/pq

=pq/pq

=1