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Question

If pth term of an A.P is q and qth term is p, then nth term is

A
(p+qpq)n
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B
(pqpq)n
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C
pqn
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D
p+qn
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Solution

The correct option is D p+qn
According to the question
Tp=a+(p1)d=q ...(1)
and
Tq:a+(q1)d=p ...(2)
By subtracting (2) from (1), we get
(p1)d(q1)d=qp
d((p1)(q1))=(qp)
d(p1q+1)=(qp)
d(pq)=(qp)
So d=1 ...(3)
Putting value of d in (1) , we get
a+(p1)1=q
ap+1=q
So, a=(q+p1)...(4)
Now, we know that
tn=a+(n1)d
By putting the value of a and d, we get
tn=(p+q1)+(n1)1
=p+q1n+1
tn=p+qn

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