Question

if the pth term of an a.p is 1/q and qth term of an a.p is 1/p then what is the sum of pq term is:​

Answer 1

Answer:

Step-by-step explanation:

1.3K answers

356.7K people helped

Given pth term = 1/q

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

aq + (pq - q)d = 1  --- (1)

Similarly,  

ap + (pq - p)d = 1  --- (2)

From (1) and (2), we get

aq + (pq - q)d = ap + (pq - p)d  

aq - ap = d[pq - p - pq + q]

a(q - p) = d(q - p)

Therefore, a = d

Equation (1) becomes,

dq + pqd - dq = 1  

d = 1/pq

Hence a = 1/pq

Consider, Spq = (pq/2)[2a + (pq - 1)d]

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

       

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

         

                       = (1/2)[pq + 1]

Answer 2

Answer:

refer to the attachment for the explanation