Concept: 2 Marks
Application: 2 Marks
Given, Sp=a,Sq=b,Sr=c
Let A and D be the first term and the common difference of the A.P.
Sp=a=p2(2A+(p−1)D)
⇒ap=A+(p−1)D2...(i)
Sq=b=q2(2A+(q−1)D)
⇒bq=A+(q−1)D2...(ii)
Sr=c=r2(2A+(r−1)D)
⇒cr=A+(r−1)D2...(iii)
E=ap(q−r)+bq(r−p)+cr(p−q)
=(A+(p−1)D2)(q−r)+(A+(q−1)D2)(r−p)+(A+(r−1)D2)(p−q) [From (i), (ii) and (iii)]
=A(q−r+r−p+p−q)+D2[(p−1)(q−r)+(q−1)(r−p)+(r−1)(p−q)]
=A(0)+D2(0)
=0