Question

if the pth ,qth and rth term of an ap are a,b,c resp.,show that a(q-r)+b(r-p)+c(p-q)​

Answer 1

Step-by-step explanation:

Ap=a+(p-1)d =a ---(1). Aq=a+(q-1)d=b ----(2). Ar=a+(r-1)d=c. --(3) . equation (2) -(3) so, a+(q-1)d -{a+(r-1)d= b-c....that is (q-r)=b-c----(4).... then eq --(3) - (1) ,we get ( r-p)=c-a -(5). similarly eq (1) -(2) we get (p-q )=a-b -(6) .... Now add eq (4),(5) and (6) and multiply a with eq (1) ,multiply b with equation (5) and finally multiply c with equation (6)....

You will get the answer..