Question

If Pth term of an AP is1/q and Qth term is 1/p,then show that it's (pq)th term is 1

Answer 1

Hi Nitesh ,

we know that
a+(n-1)d = nth term of an AP

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

To prove:
a+(pq-1)d = 1

Solution:
from (1) and (2)
aq + pqd - qd = 1
ap + pqd - pd = 1

equating above two equations , since they both are equal to 1
aq + pqd - qd = ap + pqd - pd
a(q-p) = d(q-p)
a = d

now substituting 'a=d' in (1)
a+(p-1)a = 1/q
a(1+p-1) = 1/q
ap = 1/q
apq = 1

LHS
= a+(pq-1)d
= a+(pq-1)a
= a(1+pq-1)
= apq
= 1
= RHS

Hence proved.

Hope it helped.
Let me know if any doubts.
Cheers !!!

Answer 2

Here's your answer

Hope it helps you

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