Question

If the pth, qth and rth terms are P, Q, R respectively.
Prove that P (Q – R) + Q (R –P) + R (P – Q) = 0.

Answer 1

Explanation:

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Answer 2

Answer:

ANSWER

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

T (p) =a=A+(p−1)D=(A−D)+pD-------------- (1)

T (q) =b=A+(q−1)D=(A−D)+qD -----------------(2)

T(r) =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.