Question

if pth term of an AP is 1/q and qth term of an AP is 1/p, then find the sum of pqth term.​

Answer 1

Step-by-step explanation:

So this is the answer

Answer 2

pth term

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

aq + (pq - q) * d = 1

qth term

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

ap + (pq - p) * d = 1

We have to solve pth term and qth term:

=> aq + (pq - q) * d = ap + (pq - p) * d

=> aq + pqd - qd = ap + pqd - pd

=> aq - ap = qd - pd

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

=> a = d

Place a value in pth term:

=> aq + (pq - q) * d = 1

=> dq + (pq - q) * d = 1

=> dq + pqd - dq = 1

=> pqd = 1

=> d = (1/pq)

Since a = d.

So, a = (1/pq)

Sum of pqth term :

=> (pq/2)[2a + (pq - 1) * (1/pq)]

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

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

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

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

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

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