#### Question

Sum of the first *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`

#### Solution

Let *a*_{1} and *d* be the first term and the common difference of the A.P. respectively.

According to the given information

Equating both the values of *d* obtained in (4) and (5), we obtain

aq - bppqp - q = br - qcqrq - r⇒aq - bppp - q = br - qcrq - r⇒rq - raq - bp = pp - qbr - qc⇒raq - bpq - r = pbr - qcp - q⇒aqr - bprq - r = bpr - cpqp - q

Dividing both sides by *pqr*, we obtain

Is there an error in this question or solution?

Solution Sum of the First 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 Concept: Arithmetic Progression (A.P.).