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Question

If the sum of p terms of an A.P. is q and the sum of q terms is p, then the sum of p+q terms will be

A

0

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B

p - q

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C

p + q

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D

- (p + q)

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Solution

The correct option is D: (p+q)

We know that the sum of n terms of an A.P is given by Sn=n2[2a+(n1)d]

Sum of p terms is given

Sp=q

p2[2a+(p1)d]=q

2ap+(p1)pd=2q....(i)

And, Sum of q terms is given as

Sq=p

q2{2a+(q1)d}=p

2aq+(q1)qd=2p....(ii)

on Subtracting eq.(ii) from eq.(i), we get

2ap+(p1)pd[2aq+(q1)qd]=2q2p

2ap+(p1)pd2aq(q1)qd=2q2p

2a(pq)+p2dpdq2d+qd=2(pq)

2a(pq)+p2dq2d(pq)d=2(pq)

2a(pq)+(p2q2)d(pq)d=2(pq)

2a(pq)+(pq)(p+q)d(pq)d=2(pq) [(a2b2)=(ab)(a+b)]

2a+(p+q)dd=2 [cancelling (pq) from both sides]

2a+(p+q1)d=2(iii)

Now, we have to fing sum of (p+q) terms

Sp+q=(p+q)2[2a+(p+q1)d]

=(p+q)2[2] [Using eq.(iii)]

=(p+q)


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