Question

(c) If the sums of p. q and r terms of an A.P. are a, b and c respectively, prove that:
a/p(q-r)+ b/q(r-p)+c/r(p-q)=0​

Answer 1

Answer:

Hope it will help you .........

Answer 2

Answer:

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.

                                                Hence, Proved.