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 if the pth, qth and rth term of an AP...
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Sun March 20, 2011 By: Waryaam Singh
if the pth, qth and rth term of an AP are x,y and z resp.show that x(qr)+y(rp)+z(pq)=0
Expert Reply
Dear Student,
Here is the solution to your problem:
Let a and d be ist term and common difference of the series AP
Then
x = a+(p1).d.......(1)
y = a+(q1).d.......(2)
z = a+(r1).d........(3)
subtracting 2 from 1, 3 from 2 and 1st from 3rd we get
xy = (pq).d......(4)
yz = (qr).d........(5)
zx = (rp).d.......(6)
multiply 4,5,6 by z,x,y respectively we have
z.(xy) = z.(pq).d......(4)
x.(yz) = x.(qr).d........(5)
y.(zx) = y.(rp).d.......(6)
x(qr).d+y(rp).d+z(pq).d = 0
(x(qr)+y(rp)+z(pq)).d = 0
Now since d is common difference it should be non zero hence
x(qr)+y(rp)+z(pq)= 0
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