Question

The pth term of an A.P is 1/q and the qth term is 1/p Find (p+q)th term and (pq)th term.​

Answer 1

Answer:

Let pth term of AP be ‘Ap' and qth term of AP be ‘Aq’

Therefore, Ap = a+ (p-1)d=1/q….(i)

Aq = a+(q-1)d=1/p ….(ii)

Subtracting equation (ii) from (i)

d[(p-1)-(q-1)] = 1/q-1/p,

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

d = 1/pq ….(iii)

Substituting equation (iii) in (i)

a+(p-1)/pq = 1/n,

a = 1/q[1-(p-1)/p],

a = 1/pq ….(iv)

Now Apq i.e the pqth term of AP = a+(pq-1)d,

Substitute equation (iii) and (iv) in Apq,

1/pq+(pq-1)/pq = 1/pq[1+(pq-1)] = pq/pq = 1,

then the pq term = 1

sum of pq term :-

Apq = pq/2 ( 2/pq + (pq-1)1/pq

= 1 + (pq)/2 - 1/2

= pq /2 + 1/2

= 1/2 (pq + 1)