Question

If pth,qth and rth terms of an a.p. are a,b, c respectively, then show that a(q - r)+b(r - p)+c(p - q) is

Answer 1

Answer:

0

Step-by-step explanation:

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

$A_p = A + (p-1)*D=a\\A_q=A+(q-1)*D=b\\A_r=A+(r-1)*D=c$

By substituting in the problem, we get:

$a(q-r)+b(r-p)+c(p-q)\\\\=(A+(p-1)*D)(q-r)\\+(A+(q-1)*D)(r-p)\\ +(A+(r-1)*D)(p-q)\\\\=Aq+pq-Dq-Ar-pr+Dr\\+Ar+qr-Dr-Ap-pq+Dp\\+Ap+rp-Dp-Aq-qr+Dq\\\\=0$