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QUESTION = The pth, qth and rth terms of an A.P. are a,b,c respectively. Show that (a - b)r + (b - c)p+(c - a) q = 0.
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Answer 1

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Answer 2

Step-by-step explanation:

Let A be the first term and D the common difference of A.P.

Tp=a=A+(p−1)D=(A−D)+pD         (1)

Tq=b=A+(q−1)D=(A−D)+qD        ..(2)

Tr=c=A+(r−1)D=(A−D)+rD       ..(3)

Here we have got two unknowns A and D which are to be eliminated.

We multiply (1),(2) and (3) by q−r,r−p and p−q respectively and add:

a(q−r)+b(r−p)+c(p−q)

=(A−D)[q−r+r−p+p−q]+D[p(q−r)+q(r−p)+r(p−q)]=0.